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Wyświetlanie 1-15 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
Wyświetlanie 1-15 z 28

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