Variational Approach for Tempered Fractional Sturm–Liouville Problem

Abstract

In this paper, we study the properties of eigenvalue for the regular tempered fractional Sturm–Liouville problem (TFSLP) of order μ. Using a fractional variational approach, we show that the set of eigenvalues for TFSLP are infinite, and correspond to unique eigenfunctions. We establish that the eigenvalues of the problem are distinct, and the corresponding eigenfunctions are orthogonal to each other. We also show that the minimum value of the functional corresponding to TFSLP is the lowest eigenvalue. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.