Numerical Solution of Fractional Integro-Differential Equations by Laplace Transform Method Using Shifted Chebyschev Polynomials

Student: Emmanuel Oluwadamilola Olabamidele (Project, 2025)
Department of Pure and Applied Mathematics
University of Ilorin, Kwara State

Abstract

This work presents a numerical method for solving fractional integro-differential equations
(FIDEs) which combine differential and Fredholm-Volterra integral components. The proposed approach leverages the Laplace transform to convert the FIDE into an algebraic
equation in the Laplace domain, thereby simplifying its structure. To obtain the numerical
solution, shifted Chebyshev polynomials are employed as basis functions to approximate
the unknown function. The assumed solution, obtained after applying the inverse Laplace
transform, is then substituted into the fractional integro-differential equation. This process
directly leads to a system of algebraic equations, allowing for the determination of the coefficients of the Chebyshev polynomial expansion. This system is efficiently solved using
Maple software. Numerical examples are provided to demonstrate the efficacy of the proposed method, showing that the obtained solutions converge well to the exact solution, and
the corresponding errors are found to be moderate, affirming the accuracy and applicability
of the technique.

Keywords
numerical solution fractional integro-differential equations laplace transform method shifted chebyschev
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