Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

Agnieszka B. Malinowska; Tatiana Odzijewicz; Anna Poskrobko

doi:10.34768/amcs-2023-0025

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Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

International Journal of Applied Mathematics and Computer Science

Volume 33 (2023): Issue 3 (September 2023)

By: Agnieszka B. Malinowska, Tatiana Odzijewicz and Anna Poskrobko

Open Access

|Sep 2023

Abstract

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.

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Articles in this issue

DOI: https://doi.org/10.34768/amcs-2023-0025 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X

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Language: English

Page range: 349 - 359

Submitted on: Oct 12, 2022

Accepted on: Apr 12, 2023

Published on: Sep 21, 2023

Published by: University of Zielona Góra

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

anomalous diffusion,

fractional diffusion equations,

Related subjects:

© 2023 Agnieszka B. Malinowska, Tatiana Odzijewicz, Anna Poskrobko, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 33 (2023): Issue 3 (September 2023)