Regular fractional Sturm-Liouville problem with discrete spectrum: Solutions and applications

Author

Klimek, Malgorzata ; Blasik, Marek

Author_Institution

Inst. of Math., Czestochowa Univ. of Technol., Czestochowa, Poland

fYear

2014

fDate

23-25 June 2014

Firstpage

1

Lastpage

6

Abstract

In the paper, we consider a regular fractional Sturm-Liouville problem with left and right Caputo derivatives of order in the range (1/2, 1). It depends on an arbitary positive continuous function and obeys the mixed boundary conditions defined on a finite interval. We prove that it has an infinite countable set of positive eigenvalues and its continuous eigenvectors form a basis in the space of square-integrable functions. Eigenfunctions are then applied to solve 1D and 2D anomalous diffusion equations with variable diffusivity.

Keywords

differential equations; eigenvalues and eigenfunctions; 1D anomalous diffusion equations; 2D anomalous diffusion equations; Caputo derivatives; arbitary positive continuous function; continuous eigenvectors form; discrete spectrum; eigenfunctions; finite interval; fractional Sturm-Liouville problem; infinite countable set; mixed boundary conditions; positive eigenvalues; square-integrable functions; variable diffusivity; Boundary conditions; Differential equations; Eigenvalues and eigenfunctions; Equations; Integral equations; Kernel; Mathematical model;

fLanguage

English

Publisher

ieee

Conference_Titel

Fractional Differentiation and Its Applications (ICFDA), 2014 International Conference on

Conference_Location

Catania

Type

conf

DOI

10.1109/ICFDA.2014.6967383

Filename

6967383