Eigenvalues of fractional Sturm-Liouville problems by successive method

Document Type : Research Paper

Authors

1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

2 Department of Applied Mathematics, Mathematical Science Faculty, University of Tabriz, Tabriz, Iran.

3 Department of Mathematics, Sahand University of Technology, Tabriz, Iran.

Abstract

In this paper, we consider a fractional Sturm-Liouville equation of the form, − cDα 0+ ◦ Dα 0+ y(t) + q(t)y(t) = λy(t), 0 < α < 1, t ∈ [0, 1], with Dirichlet boundary conditions I 1−α 0+ y(t)|t=0 = 0, and I 1−α 0+ y(t)|t=1 = 0, where, the sign ◦ is composition of two operators and q ∈ L2 (0, 1), is a real valued potential function. We use a recursive method based on Picard’s successive method to find the solution of this problem. We prove the method is convergent and show that the eigenvalues are obtained from the zeros of the Mittag-Leffler function and its derivatives.

Keywords