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    Wyświetlanie 1-28 z 28
    Tytuł:
    System of boundary random fractional differential equations via Hadamard derivative
    Autorzy:
    Malki, Zakaria
    Berhoun, Farida
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/1797181.pdf
    Data publikacji:
    2021-04-14
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Random fractional differential equation
    Hadamard fractional differential equation
    existence
    fixed point
    vector metric space
    Opis:
    We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2021, 20; 17-41
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive solutions of a singular fractional boundary value problem with a fractional boundary condition
    Autorzy:
    Lyons, J. W.
    Neugebauer, J. T.
    Powiązania:
    https://bibliotekanauki.pl/articles/255965.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential equation
    singular problem
    fixed point
    Opis:
    For α ∈ (1,2] the singular fractional boundary value problem [formula] satisfying the boundary conditions [formula] where β ∈ (0,α - 1], μ ∈ (0,α - 1], and [formula] are Riemann-Liouville derivatives of order α, β, and μ respectively, is considered. Here ƒ satisfies a local Carathéodory condition, and ƒ (t, x, y) may be singular at the value 0 in its space variable x. Using regularization and sequential techniques and Krasnosel’skii’s fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
    Źródło:
    Opuscula Mathematica; 2017, 37, 3; 421-434
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New perspectives of analog and digital simulations of fractional order systems
    Autorzy:
    Charef, A.
    Charef, M.
    Djouambi, A.
    Voda, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/229183.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    adjustable fractional operators
    Charef approximation
    fractional differential equation
    ractional integrator
    fractional systems
    Opis:
    In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques
    Źródło:
    Archives of Control Sciences; 2017, 27, 1; 91-118
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the transient state in RCα circuit at periodic voltage excitation
    Autorzy:
    Jakubowska, A.
    Walczak, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/97447.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional-order differential equation
    transient state
    supercapacitor
    Opis:
    The paper describes the results of analysis of the transient state in a simple series RCα circuit with supercapacitor. A simple fractional-order supercapacitor model has been introduced to the analysis. The considered system has been supplied by a periodic voltage source. Selected results of the simulation studies, carried out in Mathematica, Maple and PSpice have also been presented.
    Źródło:
    Computer Applications in Electrical Engineering; 2015, 13; 42-50
    1508-4248
    Pojawia się w:
    Computer Applications in Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of three solutions for impulsive nonlinear fractional boundary value problems
    Autorzy:
    Heidarkhani, S.
    Ferrara, M.
    Caristi, G.
    Salari, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/254791.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential equation
    impulsive condition
    classical solution
    variational methods
    critical point theory
    Opis:
    In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
    Źródło:
    Opuscula Mathematica; 2017, 37, 2; 281-301
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
    Autorzy:
    Nowak, T. K.
    Duzinkiewicz, K.
    Piotrowski, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/229399.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional differential equation
    fractional derivatives and integrals
    system of equations
    nuclear reactor
    neutron point kinetics
    Opis:
    This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
    Źródło:
    Archives of Control Sciences; 2014, 24, 2; 129-154
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line
    Autorzy:
    Boucenna, Amina
    Moussaoui, Toufik
    Powiązania:
    https://bibliotekanauki.pl/articles/729493.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential equation
    half-line
    Krasnoselsk'ii's fixed point theorem
    existence
    positive solution
    Opis:
    The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 169-189
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical solution of the time fractional Fokker-Planck equation
    Autorzy:
    Sutradhar, T.
    Datta, B. K.
    Bera, R. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/955129.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Fokkera-Plancka
    równania różniczkowe
    mechanika stosowana
    Fokker-Planck equation
    Adomian decomposition method
    fractional calculus
    fractional differential equation
    Opis:
    A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2014, 19, 2; 435-440
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The existence of consensus of a leader-following problem with Caputo fractional derivative
    Autorzy:
    Schmeidel, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/254771.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    leader-following problem
    Caputo fractional differential equation
    consensus, nonlinear system Schauder fixed point theorem
    Opis:
    n this paper, consensus of a leader-following problem is investigated. The leader-following problem describes a dynamics of the leader and a number of agents. The trajectory of the leader is given. The dynamics of each agent depends on the leader trajectory and others agents' inputs. Here, the leader-following problem is modelled by a system of nonlinear equations with Caputo fractional derivative, which can be rewritten as a system of Volterra equations. The main tools in the investigation are the properties of the resolvent kernel corresponding to the Volterra equations, and Schauder fixed point theorem. By study of the existence of an asymptotically stable solution of a suitable Volterra system, the sufficient conditions for consensus of the leader-following problem are obtained.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 77-89
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the transient state in a circuit with supercapacitor
    Autorzy:
    Jakubowska, A.
    Walczak, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/377512.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional-order differential equation
    first-order RCα circuit
    supercapacitor
    Opis:
    The paper presents an analysis of the transient state in a simple circuit of RCα class with a supercapacitor. The behavior of supercapacitors differs from that of classic capacitors, which influences voltage and current waveforms in circuits containing them. The waveforms are described by relations of fractional-order integral-differential calculus. A simple fractional-order supercapacitor model, including its series internal resistance, has been assumed for the analysis. The obtained solution of the fractional-order differential equation describing the examined circuit is presented. The impact of different values of the parameter α on the solution has been analyzed too. The derived relations are illustrated by simulation examples for the circuit powered by a DC voltage source. This situation describes the supercapacitor charging process. Its charging time depends mainly on the value of fractional-order parameter α of the supercapacitor.
    Źródło:
    Poznan University of Technology Academic Journals. Electrical Engineering; 2015, 81; 71-77
    1897-0737
    Pojawia się w:
    Poznan University of Technology Academic Journals. Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional boundary value problems on the half line
    Autorzy:
    Frioui, A.
    Guezane-Lakoud, A.
    Khaldi, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/255663.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    boundary value problem at resonance
    existence of solution
    unbounded interval
    coincidence degree of Mawhin
    fractional differential equation
    Opis:
    In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.
    Źródło:
    Opuscula Mathematica; 2017, 37, 2; 265-280
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Matrix Mittag‑Leffler function in fractional systems and its computation
    Autorzy:
    Matychyn, I.
    Onyshchenko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/200538.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    matrix Mittag‑Leffler function
    Jordan canonical form
    fractional calculus
    fractional differential equation
    równanie różniczkowe cząstkowe
    funkcja Mittag-Lefflera
    rozkład Jordana
    Opis:
    Matrix Mittag‑Leffler functions play a key role in numerous applications related to systems with fractional dynamics. That is why the methods for computing the matrix Mittag‑Leffler function are so important. The matrix Mittag‑Leffler function is a generalization of matrix exponential function. This implies that some of numerous existing methods for computing the matrix exponential can be adapted for matrix Mittag‑Leffler functions as well. Unfortunately, the technique of scaling and squaring, widely used in computing of the matrix exponential, cannot be applied to matrix Mittag‑Leffler functions, as the latter do not possess the semigroup property. Here we describe a method of computing the matrix Mittag‑Leffler function based on the Jordan canonical form representation. This method is implemented with Matlab code [1].
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 495-500
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical Solution to Linear Conformable Fractional Partial Differential Equations
    Autorzy:
    Dixit, Ajay
    Ujlayan, Amit
    Powiązania:
    https://bibliotekanauki.pl/articles/1159232.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Conformable fractional derivative
    Fractional partial differential equation
    Katugampola’s derivative
    Method of separation of variables
    Opis:
    An analytical solution is better than an approximate or series solution of a problem. Here we develop an analytical formulation to solve linear fractional order partial differential equations with given boundary conditions. We discuss the method for the simultaneous fractional derivative, in space as well as time and up to order two. Examples reflect the effectiveness and simplicity of the method. First we convert the fractional derivative into integer order derivative and then use method of separation of variables in usual sense to get the complete solution. The fractional derivative has been taken in the sense of Katugampola’s derivative.
    Źródło:
    World Scientific News; 2018, 113; 49-56
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the semi-analytic technique to deal with nonlinear fractional differential equations
    Autorzy:
    Khirsariya, Sagar R.
    Rao, Snehal B.
    Powiązania:
    https://bibliotekanauki.pl/articles/2202059.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equation
    logistic equation
    Fornberg-Whitham equation
    homotopy perturbation method
    Sawi transform
    ułamkowe równanie różniczkowe
    równanie logistyczne
    równanie Fornberga-Whithama
    metoda perturbacji homotopii
    Opis:
    In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 17--30
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fixed terminal time fractional optimal control problem for discrete time singular system
    Autorzy:
    Chiranjeevi, Tirumalasetty
    Devarapalli, Ramesh
    Babu, Naladi Ram
    Vakkapatla, Kiran Babu
    Rao, R. Gowri Sankara
    Garcìa Màrquez, Fausto Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/2175112.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order differential equation
    discrete time singular system
    fractional derivative
    linear quadratic optimal control problem
    Opis:
    This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
    Źródło:
    Archives of Control Sciences; 2022, 32, 3; 489--506
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence, uniqueness and parameter perturbation analysis results of a fractional integro-differential boundary problem
    Autorzy:
    Zhang, Nan
    Zhang, Lingling
    Ngungu, Mercy
    Adeniji, Adejimi
    Addai, Emmanuel
    Powiązania:
    https://bibliotekanauki.pl/articles/27311450.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    stability analysis
    fractional differential equation
    integro-differential boundary condition
    existence
    uniqueness
    parameter perturbations
    istnienie
    jednoznaczność
    analiza stabilności
    zaburzenia parametrów
    ułamkowe równanie różniczkowe
    warunek brzegowy całkowo-różniczkowy
    Opis:
    In the formulation, the existence, uniqueness and stability of solutions and parameter perturbation analysis to Riemann-Liouville fractional differential equations with integro-differential boundary conditions are discussed by the properties of Green’s function and cone theory. First, some theorems have been established from standard fixed point theorems in a proper Banach space to guarantee the existence and uniqueness of positive solution. Moreover, we discuss the Hyers-Ulam stability and parameter perturbation analysis, which examines the stability of solutions in the presence of small changes in the equation main parameters, that is, the derivative order η, the integral order β of the boundary condition, the boundary parameter ξ , and the boundary value τ. As an application, we present a concrete example to demonstrate the accuracy and usefulness of the proposed work. By using numerical simulation, we obtain the figure of unique solution and change trend figure of the unique solution with small disturbances to occur in different kinds of parameters.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e145938
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical solution of a fractional coupled system with the Caputo-Fabrizio fractional derivative
    Autorzy:
    Mansouri, Ikram
    Bekkouche, Mohammed Moumen
    Ahmed, Abdelaziz Azeb
    Powiązania:
    https://bibliotekanauki.pl/articles/2202061.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Caputo-Fabrizio fractional derivative
    fractional integral
    coupled system
    fractional differential equation
    fixed point
    Adomian decomposition method
    pochodna ułamkowa Caputo-Fabrizio
    całkowanie ułamkowe
    system sprzężony
    ułamkowe równanie różniczkowe
    punkt stały
    metoda dekompozycji Adomiana
    Opis:
    Within this work, we discuss the existence of solutions for a coupled system of linear fractional differential equations involving Caputo-Fabrizio fractional orders. We prove the existence and uniqueness of the solution by using the Picard-Lindel ̈of method and fixed point theory. Also, to compute an approximate solution of problem, we utilize the Adomian decomposition method (ADM), as this method provides the solution in the form of a series such that the infinite series converge to the exact solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 46--56
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional heat conduction in a rectangular plate with bending moments
    Autorzy:
    Warbhe, Shrikant
    Powiązania:
    https://bibliotekanauki.pl/articles/1839729.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Mittag-Leffler function
    integral transform
    fractional partial differential equation
    fractional derivatives
    fractional integrals
    ułamkowe równanie różniczkowe cząstkowe
    funkcja Mittag-Lefflera
    pochodna ułamkowa
    naprężenia termiczne
    przewodzenia ciepła
    transformata całkowa
    Opis:
    In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 115-126
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional heat conduction in a rectangular plate with bending moments
    Autorzy:
    Warbhe, Shrikant
    Powiązania:
    https://bibliotekanauki.pl/articles/1839752.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Mittag-Leffler function
    integral transform
    fractional partial differential equation
    fractional derivatives
    fractional integrals
    ułamkowe równanie różniczkowe cząstkowe
    funkcja Mittag-Lefflera
    pochodna ułamkowa
    naprężenia termiczne
    przewodzenia ciepła
    transformata całkowa
    Opis:
    In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 115-126
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillation of time fractional vector diffusion-wave equation with fractional damping
    Autorzy:
    Ramesh, R.
    Harikrishnan, S.
    Nieto, J. J.
    Prakash, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255843.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional diffusion-wave equation H-oscillation
    vector differential equation
    Opis:
    In this paper, sufficient conditions for H-oscillation of solutions of a time fractional vector diffusion-wave equation with forced and fractional damping terms subject to the Neumann boundary condition are established by employing certain fractional differential inequality, where H is a unit vector in Rn. The examples are given to illustrate the main results.
    Źródło:
    Opuscula Mathematica; 2020, 40, 2; 291-305
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergences Analysis from the Solution Function of the Riccati Fractional Differential Equation by Using Modified Homotopy Perturbation Method
    Autorzy:
    Sevira, Nurazizah M.
    Rusyaman, Endang
    Firdaniza, Firdaniza
    Subiyanto, Subiyanto
    Supian, Sudradjat
    Powiązania:
    https://bibliotekanauki.pl/articles/1059423.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Convergent
    Differential Equation
    Fractional
    Modified Homotopy Perturbation Method
    Riccati
    Opis:
    A Fractional differential equation is an equation that contains derivatives with an order of fractional numbers. Same with natural number order differential equations, this type of equation is divided into linear and nonlinear fractional differential equations. One of the equations that include nonlinear fractional differential equation is Riccati fractional differential equation (RFDE). Various methods have been applied to find solutions for fractional differential equations Riccati, one of them is the Modified Homotopy Perturbation Method (MHPM) which is a modification of the Homotopy Perturbation Method by Zaid Odibat and Shaher Momani. In this study, the MHPM was used to find solutions for fractional differential equations Riccati, which were then used to analyze the convergence of the function sequences of the solution. The result shows us that the order sequence of Riccati fractional differential equation which converges to a number causes the solution function sequence of Riccati fractional differential equation will converge to the function of the solution of Riccati fractional differential equation with the order of this number.
    Źródło:
    World Scientific News; 2019, 128, 2; 71-87
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear dynamic analysis of viscoelastic membranes described with fractional differential models
    Analiza nieliniowej dynamiki lepko-sprężystych powłok opisanych modelem o pochodnej ułamkowej
    Autorzy:
    Katsikadelis, J. T.
    Powiązania:
    https://bibliotekanauki.pl/articles/280344.pdf
    Data publikacji:
    2012
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    viscoelastic membranes
    nonlinear vibrations
    nonlinear fractional differential equations
    analog equation method
    boundary elements
    Opis:
    The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement components. These equations are solved using the BEM for fractional partial differential equations developed recently by Katsikadelis. Without excluding other viscoelastic models, the herein employed material is the Kelvin-Voigt model with a fractional order derivative. Numerical examples are presented which not only demonstrate the efficiency of the solution procedure, but also give a better insight into this complicated but very interesting response of structural viscoelastic membranes. It is worth noting that in case of resonance, phenomena similar to those of the Duffing equation are observed.
    W pracy przedstawiono analizę dynamiki płaskiej powłoki lepko-sprężystej po wstępnym ugięciu. Reologiczny model materiału powłoki opisano równaniem o pochodnych ułamkowych. Powłokę poddano płaskiemu, poprzecznemu obciążeniu zewnętrznemu. Zagadnienie dynamiki ujęto układem trzech sprzężonych nieliniowych równań różniczkowych typu hiperbolicznego o pochodnych ułamkowych. Równania rozwiązano metodą elementów brzegowych (BEM) sformułowaną przez autora właśnie dla układów opisanych pochodnymi ułamkowymi. W prezentowanej pracy założono, że powłoka wykonana jest z lepko-sprężystego materiału Kelvina-Voigta o pochodnej ułamkowej, choć samo sformułowanie BEM nie wyklucza możliwości analizy innych modeli reologicznych. Przedstawiono kilka przykładów symulacji numerycznych pokazujących efektywność zastosowanej metody rozwiązywania oraz dających lepszy obraz interesującej, lecz skomplikowanej dynamiki lepko-sprężystych powłok. Warto również podkreślić, że w warunkach rezonansowych odnotowano zjawiska podobne do obserwowanych w układzie Duffinga.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2012, 50, 3; 743-753
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion
    Autorzy:
    Borkowski, D.
    Jańczak-Borkowska, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254731.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    backward stochastic differential equation
    fractional Brownian motion
    backward stochastic variational inequalities
    subdifferential operator
    Opis:
    We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.
    Źródło:
    Opuscula Mathematica; 2018, 38, 3; 307-326
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The fourth-order ordinary differential equation with the fractional initial/boundary conditions
    Autorzy:
    Siedlecki, Jarosław
    Powiązania:
    https://bibliotekanauki.pl/articles/122929.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional calculus
    ordinary differential equation
    analytical solution
    rachunek ułamkowy
    równanie różniczkowe zwyczajne
    rozwiązanie analityczne
    warunek brzegowy
    Opis:
    The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 79-87
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The fourth-order ordinary differential equation with the fractional initial/boundary conditions
    Autorzy:
    Siedlecki, Jarosław
    Powiązania:
    https://bibliotekanauki.pl/articles/1839799.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional calculus
    ordinary differential equation
    analytical solution
    rachunek ułamkowy
    równanie różniczkowe zwyczajne
    rozwiązanie analityczne
    warunek brzegowy
    Opis:
    The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 79-87
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical computations of the fractional derivative in IVPS, examples in MATLAB and Mathematica
    Obliczenia numeryczne pochodnej ułamkowego rzędu w zagadnieniach początkowych, przykłady w programach MATLAB i Mathematica
    Autorzy:
    Sowa, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/408650.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
    Tematy:
    fractional calculus
    numerical analysis
    circuit analysis
    integro-differential equation
    pochodna ułamkowego rzędu
    analiza numeryczna
    analiza obwodów
    równanie całkowo-różniczkowe
    Opis:
    The paper concerns a numerical method that deals with the computations of the fractional derivative in Caputo and Riemann-Liouville definitions. The method can be applied in time stepping processes of initial value problems. The name of the method is SubIval, which is an acronym of its previous name – the subinterval-based method. Its application in solving systems of fractional order state equations is presented. The method has been implemented into an ActiveX DLL. Exemplary MATLAB and Mathematica codes are given, which provide guidance on how the DLL can be used.
    Artykuł dotyczy numerycznej metody, którą wykorzystać można do obliczeń pochodnej ułamkowego rzędu w definicji Caputo i Riemanna-Liouville’a. Metoda ta może być wykorzystana przy rozwiązywaniu zagadnień początkowych. Metoda nosi nazwę SubIval, co jest akronimem jej poprzedniej, anglojęzycznej nazwy „subinterval-based method” (metoda podprzedziałów). Przedstawiono jej zastosowanie w rozwiązywaniu równań stanu ułamkowego rzędu. Metoda została zaimplementowana w bibliotece DLL z obsługą ActiveX. Przedstawiono przykładowe kody obliczeniowe (w oprogramowaniach MATLAB i Mathematica), które zawierają wskazówki dotyczące zastosowania biblioteki.
    Źródło:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2017, 7, 3; 19-22
    2083-0157
    2391-6761
    Pojawia się w:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The controllability of nonlinear implicit fractional delay dynamical systems
    Autorzy:
    Joice Nirmala, R.
    Balachandran, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/331001.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    controllability
    fractional delay
    differential equation
    Mittag-Leffler function
    fixed point theorem
    sterowalność
    opóźnienie ułamkowe
    równanie różniczkowe
    funkcja Mittag-Lefflera
    Opis:
    This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 501-513
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and convergence results for Caputo fractional Volterra integro-differential equations
    Autorzy:
    Hamoud, A. A.
    Bani Issa, M. Sh.
    Ghadle, K. P.
    Abdulghani, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052432.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    homotopy analysis method
    Caputo fractional derivative
    Volterra integro-differential equation
    approximate solution
    homotopijna metoda analizy
    pochodna ułamkowa Caputo
    równanie różniczkowe Volterry
    rozwiązanie przybliżone
    Opis:
    In this article, homotopy analysis method is successfully applied to find the approximate solution of Caputo fractional Volterra integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, we proved the existence and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
    Źródło:
    Journal of Mathematics and Applications; 2018, 41; 109-121
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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