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Wyświetlanie 1-15 z 52
Tytuł:
Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
Autorzy:
Benchohra, M.
Mostefai, F.
Powiązania:
https://bibliotekanauki.pl/articles/255390.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
boundary value problem
Caputo fractional derivative
measure of weak noncompactness
Pettis integrals
weak solution
Opis:
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 31-40
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses
Autorzy:
Abbas, Saïd
Benchohra, Mouffak
Abdalla Darwish, Mohamed
Powiązania:
https://bibliotekanauki.pl/articles/729578.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
fractional differential inclusion
left-sided mixed Riemann-Liouville integral
Caputo fractional order derivative
upper solution
lower solution
extremal solution
fixed point
Banach algebras
not instantaneous impulses
Opis:
In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 155-179
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses
Autorzy:
Abbas, Saïd
Benchohra, Mouffak
Powiązania:
https://bibliotekanauki.pl/articles/729279.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive hyperbolic differential inclusion
fractional order
upper solution
lower solution
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
fixed point
Opis:
In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 141-161
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping
Autorzy:
Das, Deepanjan
Powiązania:
https://bibliotekanauki.pl/articles/122961.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equations
Caputo fractional derivative
generalized
differential transform method
analytic solution
ułamkowe równania różniczkowe
ułamkowa pochodna Caputo
metoda transformacji różnicowej
rozwiązanie analityczne
ułamkowe równanie różniczkowe
Opis:
In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 19-29
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption
Autorzy:
Povstenko, Y.
Klekot, J.
Powiązania:
https://bibliotekanauki.pl/articles/122778.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
non-Fourier heat conduction
Caputo fractional derivative
heat absorption
Laplace integral transform
Fourier transform
Mittag-Leffler function
przewodzenie ciepła
pochodna ułamkowa Caputo
absorpcja ciepła
transformata Laplace'a
transformata Fouriera
funkcja Mittag-Lefflera
Opis:
The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 101-112
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space
Autorzy:
Povstenko, Y.
Klekot, J.
Powiązania:
https://bibliotekanauki.pl/articles/122941.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Caputo fractional derivative
advection-diffusion equation
Laplace integral transform
Fourier sine transform
Mittag-Leffler function
pochodna rzędu ułamkowego Caputo
funkcja Mittag-Lefflera
Opis:
The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 73-83
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some new existence results and stability concepts for fractional partial random differential equations
Autorzy:
Abbas, S.
Benchohra, M.
Darwish, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/357770.pdf
Data publikacji:
2016
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
random differential equations
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
Banach space
Darboux problem
Ulam stability
równanie różniczkowe
pochodna Caputo
przestrzeń Banacha
problem Darbouxa
Opis:
In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.
Źródło:
Journal of Mathematics and Applications; 2016, 39; 5-22
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative
Autorzy:
Elkott, Ibrahim
Abdel-Latif, Mohamed S.
El-Kalla, Ibrahim L.
Abdel Kader, Abass H.
Powiązania:
https://bibliotekanauki.pl/articles/24201502.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
generalized time-fractional Caputo derivative
generalized Laplace transform
Hankel transform
diffusion-wave equation
uogólniona ułamkowa pochodna Caputo w czasie
uogólniona transformata Laplace'a
transformata Hankela
równanie fali dyfuzyjnej
Opis:
In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 5--14
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Autorzy:
Beata, Sikora
Powiązania:
https://bibliotekanauki.pl/articles/27311455.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
descriptor systems
fractional-order systems
Caputo derivative
Drazin inverse
controllability
pochodna Caputo
odwrotność Drazina
sterowalność
system deskryptorowy
system ułamkowego rzędu
Opis:
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
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:
Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
Autorzy:
Basdouri, Imed
Kasmi, Souad
Lerbet, Jean
Powiązania:
https://bibliotekanauki.pl/articles/27312007.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional-order systems
Caputo derivative
quasi-one-sided Lipschitz condition
nonlinear systems
observer design
output feedback stabilization
separation principle
Opis:
This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 55--70
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On theoretical and practical aspects of Duhamel’s integral
Autorzy:
Różański, Michał
Sikora, Beata
Smuda, Adrian
Wituła, Roman
Powiązania:
https://bibliotekanauki.pl/articles/2083463.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Duhamel’s integral
Duhamel’s principle
Duhamel’s formula
Laplace transformation
semigroup of operators
Leibniz integral rule
Volterra integral equation
Caputo fractional derivative
Opis:
The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
Źródło:
Archives of Control Sciences; 2021, 31, 4; 815-847
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
Autorzy:
Graef, John R.
Grace, Said R.
Tune, Ercan
Powiązania:
https://bibliotekanauki.pl/articles/255164.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
integro-differential equations fractional differential equations nonoscillatory solutions boundedness
Caputo derivative
Opis:
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form [formula] where t ≥ c ≥ α ∈(0, 1), η ≥ 1 is the ratio of positive odd integers, and [formula] denotes the Caputo fractional derivative of y of order α. The cases [formula] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 227-239
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On LQ optimization problem subject to fractional order irregular singular systems
Autorzy:
Muhafzan, -
Nazra, Admi
Yulianti, Lyra
Zulakmal, -
Revina, Refi
Powiązania:
https://bibliotekanauki.pl/articles/1409212.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear quadratic optimization
fractional order
irregular singular system
Caputo fractional derivative
Mittag-Leffler function
Opis:
In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.
Źródło:
Archives of Control Sciences; 2020, 30, 4; 745-756
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On fractional random differential equations with delay
Autorzy:
Vu, H.
Phung, N. N.
Phuong, N.
Powiązania:
https://bibliotekanauki.pl/articles/254723.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
sample path fractional integral
sample path fractional derivative
fractional differential equations
sample fractional random differential equations
Caputo fractional derivative
delay
Opis:
In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.
Źródło:
Opuscula Mathematica; 2016, 36, 4; 541-556
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 52

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