Direct and inverse problems of fractional Sturm–Liouville equation

Abstract

In this paper we define a fractional Sturm–Liouville problem (FSLP) on [0, 1] subject to dirichlet boundary condition. First we discretize FSLP to obtain the corresponding matrix eigenvalue problem (MEP) of finite order N. In direct problem we give an efficient numerical algorithm to make good approximations for eigenvalues of FSLP by adding a correction term to eigenvalues of MEP. For inverse problem, using the idea of correction technique, we propose an algorithm for recovering the symmetric potential function using one given spectrum. Finally, we give some numerical examples to show the efficiency of the proposed algorithm.