online read us now
Paper details
Number 3 - September 2023
Volume 33 - 2023
Applications of the fractional Sturm–Liouville difference problem to the fractional diffusion difference equation
Agnieszka B. Malinowska, Tatiana Odzijewicz, Anna Poskrobko
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 SturmꟷLiouville problem, we show that solutions of fractional diffusion difference
equations exist and are given by a finite series.
Keywords
anomalous diffusion, fractional diffusion equations, fractional calculus, difference equations