Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems

TL;DR

This paper introduces a variational approach to approximate solutions of fractional Sturm-Liouville eigenvalue problems, which are relevant in physical and engineering contexts involving anomalous diffusion.

Contribution

It formulates the fractional Sturm-Liouville problem as a constrained fractional variational principle and demonstrates its effectiveness through numerical examples.

Findings

Successful approximation of fractional Sturm-Liouville solutions

Applicable to physical models with anomalous diffusion

Numerical results validate the variational method

Abstract

The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions to this problem is of great importance. Here, we describe how the fractional Sturm-Liouville eigenvalue problem can be formulated as a constrained fractional variational principle and show how such formulation can be used in order to approximate the solutions. Numerical examples are given, to illustrate the method.