Results 61 to 70 of about 35,805 (203)

Fast, Accurate and Robust Adaptive Finite Difference Methods for Fractional Diffusion Equations: The Size of the Timesteps does Matter

, 2014
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of the number of
Quintana-Murillo, Joaquin, Yuste, Santos B.   +1 more
core   +1 more source

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

Advances in Difference Equations, 2021
In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders 0 < ϑ ≤ 1 ...
Mohammed S. Abdo, Thabet Abdeljawad, Saeed M. Ali, Kamal Shah   +3 more
doaj   +1 more source

Qualitative study on Hilfer-Katugampola fractional implicit differential equations

Open Journal of Mathematical Sciences, 2022
This paper solves implicit differential equations involving Hilfer-Katugampola fractional derivatives with nonlocal, boundary, and impulsive conditions. In addition, some sufficient conditions are formulated for the existence and uniqueness of solutions to the given problem, and Hyers-Ulam stability results are also presented.
E. M. Elsayed, S. Harikrishnan, D. Vivek, K. Kanagarajan   +3 more
openaire   +1 more source

On an explicit finite difference method for fractional diffusion equations

, 2003
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered.
Gorenflo Rudolf, Gorenflo Rudolf, L. Acedo, Morton K., Podlubny Igor, S. B. Yuste   +5 more
core   +1 more source

On nonlinear implicit fractional differential equations without compactness

The Journal of Nonlinear Sciences and Applications, 2017
Summary: The main purpose of this research paper is to develop some sufficient conditions for the existence of solution of a nonlinear problem of implicit fractional differential equations (IFDEs) with boundary conditions, using prior estimate method. The distinction of the method applied here is, it does not require compactness of the operator.
Bushnaq, Samia, Hussain, Wajid, Shah, Kamal   +2 more
openaire   +3 more sources

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

, 2017
We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian.
AA Golovin, AH Stroud, Alexandre Ern, BJ West, IG Graham, IH Sloan, IH Sloan, Krzysztof Bogdan, L Caffarelli, LR Scott, M D’Elia, Mark Ainsworth, Mark Ainsworth, MG Duffy, MM Meerschaert, P Ciarlet, Raffaella Servadei, RH Nochetto, RK Getoor, S Erichsen, SA Silling, Stefan A. Sauter, T Koto, W Hackbusch, WCH McLean, Y Yan, ZQ Chen   +26 more
core   +1 more source

Analysis of nonlinear implicit fractional differential equations with the Atangana-Baleanu derivative via measure of non-compactness

AIMS Mathematics
In this study, we proved existence results for nonlinear implicit fractional differential equations with the Caputo version of the Atangana-Baleanu derivative, subject to the boundary and nonlocal initial conditions.
Kishor D. Kucche, Sagar Sutar, K. Nisar
semanticscholar   +1 more source

Fractional SDEs with stochastic forcing: Existence, uniqueness, and approximation

Nonlinear Analysis, 2023
In this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term.
Kęstutis Kubilius
doaj   +1 more source

Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

Moroccan Journal of Pure and Applied Analysis, 2015
In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach
Benchohra Mouffak, Bouriah Soufyane
doaj   +1 more source

Integral Boundary Value Problems for Implicit Fractional Differential Equations Involving Hadamard and Caputo-Hadamard fractional Derivatives

, 2021
In this paper, we examine the existence and uniqueness of integral boundary value problem for implicit fractional differential equations (IFDE’s) involving Hadamard and Caputo-Hadamard fractional derivative.
P. Karthikeyan, R. Arul
semanticscholar   +1 more source