Numerical solution of fractional Sturm-Liouville equation in integral form

TL;DR

This paper develops a numerical method for solving fractional Sturm-Liouville equations in integral form, demonstrating its convergence through examples and providing a practical approach for such fractional differential equations.

Contribution

It introduces a novel numerical scheme for fractional Sturm-Liouville equations in integral form and discusses its convergence based on numerical experiments.

Findings

Numerical solutions effectively approximate the fractional Sturm-Liouville equations.

The proposed method converges reliably as shown by numerical results.

The integral form transformation facilitates numerical analysis of fractional differential equations.

Abstract

In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.