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Wyświetlanie 1-15 z 52
Tytuł:
Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions
Autorzy:
Zada, Akbar
Yar, Muhammad
Li, Tongxing
Powiązania:
https://bibliotekanauki.pl/articles/744661.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Tematy:
Caputo fractional derivative
Riemann–Liouville fractional integral
coupled system
existence
uniqueness
fixed point theorem
Hyers–Ulam stability
Źródło:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2018, 17
2300-133X
Pojawia się w:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
Autorzy:
Wahash, Hanan A.
Abdo, Mohammed S
Panchal, Satish K.
Powiązania:
https://bibliotekanauki.pl/articles/1839794.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equations
ψ-fractional integral and derivative
existence and Ulam-Hyers stability
fixed point theorem
równania różniczkowe ułamkowe
równania różniczkowe cząstkowe
pochodna ułamkowa
twierdzenie o punkcie stałym
pochodna ułamkowa Caputo
Opis:
In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ. The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
Autorzy:
Wahash, Hanan A.
Abdo, Mohammed S
Panchal, Satish K.
Powiązania:
https://bibliotekanauki.pl/articles/122800.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional differential equations
ψ-fractional integral and derivative
existence and Ulam-Hyers stability
fixed point theorem
równania różniczkowe ułamkowe
równania różniczkowe cząstkowe
pochodna ułamkowa
twierdzenie o punkcie stałym
pochodna ułamkowa Caputo
Opis:
In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ . The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
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
Tytuł:
Application of fractional order theory of thermoelasticity in an elliptical disk and associated thermal stresses
Autorzy:
Thakare, S.
Panke, Y.
Hadke, K.
Powiązania:
https://bibliotekanauki.pl/articles/1839826.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
naprężenia termiczne
pochodna Caputo
termosprężystość
elliptical disk
fractional order theory
Caputo derivative
integral transform
thermal stresses
thermal deflection
Opis:
In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 3; 169-180
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mittag-Leffler stability for a Timoshenko problem
Autorzy:
Tatar, Nasser-eddine
Powiązania:
https://bibliotekanauki.pl/articles/1838213.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Caputo fractional derivative
Mittag-Leffler stability
multiplier technique
resolvent operator
Opis:
A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 219-232
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized Isoperimetric FVPs Via Caputo Approach
Autorzy:
Taïeb, Amele
Dahmani, Zoubir
Powiązania:
https://bibliotekanauki.pl/articles/2188101.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
Caputo derivative
Fractional calculus of variations
isoperimetric problems
Opis:
In this paper, we study several fractional variational problems with functionals that contain n unknown functions with their higher order Caputo derivatives and Riemann–Liouville integrals. We prove generalized fractional Euler–Lagrange equations. We also study an isoperimetric problem with multiple constraints, and we find the optimality conditions. Some examples are provided to illustrate the applications of the results.
Źródło:
Universitatis Iagellonicae Acta Mathematica; 2019, 56; 23-40
2084-3828
0083-4386
Pojawia się w:
Universitatis Iagellonicae Acta Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On controllability of fractional positive continuous-time linear systems with delay
Autorzy:
Sikora, Beata
Matlok, Natalia
Powiązania:
https://bibliotekanauki.pl/articles/1409030.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional systems
positive systems
Caputo derivative
controllability
delay
Metzler matrix
Opis:
In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
Źródło:
Archives of Control Sciences; 2021, 31, 1; 29-51
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability criteria for time-delay fractional systems with a retarded state
Autorzy:
Sikora, B.
Powiązania:
https://bibliotekanauki.pl/articles/330421.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional dynamical systems
controllability criteria
delays in the state
constraints
pseudotransition matrix
Caputo derivative
układ dynamiczny ułamkowy
sterowalność
pochodna ułamkowego rzędu Caputo
Opis:
The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 521-531
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of solutions of the 1D fractional Cattaneo heat transfer equation
Autorzy:
Siedlecka, Urszula
Ciesielski, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/2175501.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
heat transfer
Cattaneo equation
fractional Caputo derivative
Laplace transform
Fourier transform
wymiana ciepła
równanie Cattaneo
pochodna ułamkowa Caputo
transformata Laplace'a
transformata Fouriera
Opis:
In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 87--98
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Heat conduction in a finite medium using the fractional single-phase-lag model
Autorzy:
Siedlecka, Urszula
Powiązania:
https://bibliotekanauki.pl/articles/200748.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
single-phase-lagging heat conduction
Caputo derivative
fractional heat conduction
przewodzenie ciepła
Pochodna Caputo
Opis:
In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 2; 401-407
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical 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:
Axisymmetric solutions to the Cauchy problem for time-fractional diffusion equation in a circle
Autorzy:
Povstenko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/121736.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
Cauchy problem
circle
Caputo fractional derivative
problem Cauchy'ego
koło
Opis:
The Cauchy problems for time-fractional diffusion equation with delta pulse initial value of a sought-for function is studied in a circle domain in the axisymmetric case under zero Dirichlet and Neumann boundary conditions, respectively. The Caputo fractional derivative is used. The Laplace and finite Hankel integral transforms are employed. The results are illustrated graphically.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2010, 15; 109-117
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Different kinds of boundary conditions for time-fractional heat conduction equation
Autorzy:
Povstenko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/121936.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
boundary conditions
heat conduction
time-fractional equation
Caputo derivative
przewodzenie ciepła
warunki brzegowe
pochodna Caputo
Opis:
The time-fractional heat conduction equation with the Caputo derivative of the order 0 ˂ α ˂ 2 is considered in a bounded domain. For this equation different types of boundary conditions can be given. The Dirichlet boundary condition prescribes the temperature over the surface of the body. In the case of mathematical Neumann boundary condition the boundary values of the normal derivative are set, the physical Neumann boundary condition specifies the boundary values of the heat flux. In the case of the classical heat conduction equation (α = 1), these two types of boundary conditions are identical, but for fractional heat conduction they are essentially different. The mathematical Robin boundary condition is a specification of a linear combination of the values of temperature and the values of its normal derivative at the boundary of the domain, while the physical Robin boundary condition prescribes a linear combination of the values of temperature and the values of the heat flux at the surface of a body.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2011, 16; 61-66
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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
Wyświetlanie 1-15 z 52

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