A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials

TL;DR

This paper introduces a more stable algorithm for computing fractional integrals of orthogonal polynomials, aiding in solving fractional differential equations with improved numerical stability.

Contribution

It presents a novel, more stable algorithm for fractional integrals of orthogonal polynomials, enhancing numerical solutions of fractional differential equations.

Findings

Algorithm demonstrates increased stability over traditional methods

Numerical examples validate the effectiveness of the proposed approach

Potential applications in solving fractional differential equations

Abstract

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving corresponding fractional differential equations. A few numerical examples are reported.