Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations

TL;DR

This paper introduces and analyzes a spectral Chebyshev-Legendre method for solving Fredholm-type fractional integro-differential equations with Caputo derivatives, demonstrating exponential error decay.

Contribution

It provides a new spectral approximation approach for fractional Fredholm equations and proves exponential convergence in the L^2-norm.

Findings

Error decays exponentially in L^2-norm

Method effectively approximates solutions with known exact solutions

Validated through numerical examples

Abstract

In this paper, we propose and analyze a spectral Chebyshev-Legendre approximation for fractional order integro-differential equations of Fredholm type. The fractional derivative is described in the Caputo sense. Our proposed method is illustrated by considering some examples whose exact solutions are available. We prove that the error of the approximate solution decay exponentially in L^2-norm.