APPLICATIONS OF THE FRACTIONAL STURM--LIOUVILLE DIFFERENCE PROBLEM TO THE FRACTIONAL DIFFUSION DIFFERENCE EQUATION.

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 Gr¨unwald 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. [ABSTRACT FROM AUTHOR]