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Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation

Malinowska Agnieszka B., Odzijewicz Tatiana, Poskrobko Anna

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 3

349--359

This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm-Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.

A numerical solution for a class of time fractional diffusion equations with delay

Pimenov V. G., Hendy A. S.

International Journal of Applied Mathematics and Computer Science

2017

Vol. 27, no. 3

477--488

This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ 2−α + h4) in L ∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.