Numerical solution for fractional variational problems using the Jacobi polynomials

TL;DR

This paper introduces a numerical method utilizing Jacobi polynomials to solve fractional variational problems, demonstrating convergence and accuracy through theoretical formulas and example comparisons.

Contribution

The paper develops a novel numerical approach based on Jacobi polynomials for fractional variational problems, including formulas for fractional derivatives and integrals, and validates convergence with examples.

Findings

The method accurately approximates solutions to fractional variational problems.

Formulas for fractional derivatives and integrals of Jacobi polynomials are established.

Numerical results show convergence and agreement with exact solutions.

Abstract

We exhibit a numerical method to solve fractional variational problems, applying a decomposition formula based on Jacobi polynomials. Formulas for the fractional derivative and fractional integral of the Jacobi polynomials are proven. By some examples, we show the convergence of such procedure, comparing the exact solution with numerical approximations.