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    Wyświetlanie 1-8 z 8
    Tytuł:
    Analytical and numerical study for a fractional boundary value problem with a conformable fractional derivative of Caputo and its fractional integral
    Autorzy:
    Bekkouche, M. Moumen
    Guebbai, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839786.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional boundary value problem
    Volterra-Fredholm integral equation
    fractional derivative
    fractional integral
    równanie całkowe Volterry-Fredholma
    ułamkowa wartość brzegowa
    pochodna ułamkowa Caputo
    Opis:
    We study the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo type, which increases the interest of this study. In order to study this problem we have introduced a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo, therefore, the proofs are based upon the reduction of the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and we have built the minimum conditions to obtain the existence and uniqueness of this solution. The analytical study is followed by a complete numerical study.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 31-42
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo
    Autorzy:
    Piotrowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/141097.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    conformable fractional derivative
    fractional electrical circuit
    different fractional order system
    Opis:
    The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
    Źródło:
    Archives of Electrical Engineering; 2018, 67, 3; 629--639
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Problems with modeling of fractional electrical circuits containing supercapacitors
    Autorzy:
    Piotrowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/378115.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional order system
    electrical circuits containing supercapacitors
    Caputo definition
    Conformable Fractional Derivative definition
    Opis:
    For proper operation, diagnostics or control, it is required to know the parameters of the supercapacitor replacement model (relationship between current and voltage at the terminals). The paper describe the bahavior of the eletrical circuit (RC) containing the supercapacitor were used the fractional derivatives of Caputo definiton and Conformable Fractional Derivative definition. Verification of the correctness of the suggested electrical circuit models was carried out a series of measurements of the system response to the given control signal. The measurement data were compared by fractionalorder derivatives: classical case, Caputo definition and CFD definition. Conducting a series of experiments with charging a supercapacitor in an RC circuit, constant control voltage from 2 V to 5 V with an exchanged external resistor, it was shown that none of the three mathematical models reflects the real behavior of the supercapacitor. It has been shown that the behavior of supercapacitor requires the use of different mathematical than fractional derivatives.
    Źródło:
    Poznan University of Technology Academic Journals. Electrical Engineering; 2020, 104; 65-74
    1897-0737
    Pojawia się w:
    Poznan University of Technology Academic Journals. Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions
    Autorzy:
    Piotrowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/378130.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    fractional order system
    Sinusoidal Signals
    Caputo definition
    conformable fractional derivative definition
    fractional electrical circuit
    Opis:
    This paper presents the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo definition and the conformable fractional derivative definition are given the solutions in the case of: 1) control in the form of sine function at zero initial states 2) control in the form of cosine function at zero initial states 3) control in the form of the sine function with phase shift at zero initial states. The solutions are shown for capacitor voltages for fractional derivative orders of 0.7; 0.8; 1.0. The results were compared using graphs.
    Źródło:
    Poznan University of Technology Academic Journals. Electrical Engineering; 2019, 97; 155-167
    1897-0737
    Pojawia się w:
    Poznan University of Technology Academic Journals. Electrical Engineering
    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:
    Analysis of positive linear continuous-time systems using the conformable derivative
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/331153.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    conformable fractional derivative
    positive linear system
    system stability
    pochodna ułamkowa
    układ liniowy dodatni
    stabilność systemu
    Opis:
    Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 2; 335-340
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of fractional electrical circuit with rectangular input signal using Caputo and conformable derivative definitions
    Autorzy:
    Piotrowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/140842.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order system
    Caputo definition
    conformable fractional definition
    fractional electrical circuit
    Opis:
    An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF definitions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
    Źródło:
    Archives of Electrical Engineering; 2018, 67, 4; 789-802
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cubic nonlinear fractional Schrödinger equation with conformable derivative and its new travelling wave solutions
    Autorzy:
    Gündoğdu, Hami
    Gözükızıl, Ömer Faruk
    Powiązania:
    https://bibliotekanauki.pl/articles/1839843.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    cubic nonlinear fractional Schrödinger equation
    travelling wave solutions
    kink solution
    soliton solution
    równanie różniczkowe zwyczajne
    roztwór solitonu
    równanie Schrödingera
    fale biegnące
    Opis:
    In the present paper, the fractional-order cubic nonlinear Schrödinger equation is considered. The Schrödinger equation with time and space fractional derivative is studied at the same time. Different types of travelling wave solutions including the kink solution, soliton solution, periodic solution, and singular solution for the mentioned equation are obtained by using the Jacobi elliptic functions expansion method. It is shown that the solutions turn into the exact solutions when the fractional orders go to 1. This method can be relied on gaining the solutions to time or space fractional order partial differential equations as well as ordinary ones. Throughout this work, the fractional derivative is given in a conformable sense.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 29-41
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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