We solve a fractional Fredholm integro-differential equation (FIDE) by operational matrix method based on the fractional derivative in the sense of Caputo of Hermite orthogonal polynomials. Decomposing the integral part and the initial conditions in terms of Hermite polynomials and using collocation method, the FIDE has been transformed to the system of linear equations in unknown Hermite coefficients. By replacing the FIDE with a set of linear algebraic equations, the complete problem was simplified. Then either approximated or exact solution is achieved by solving these algebraic equations. Some numerical examples are provided to demonstrate the efficiency of the proposed method.

fractional derivative in sense of Caputo, fractional Fredholm integro-differential equation, Hermite operation matrix.

Received: October 18, 2023; Accepted: November 6, 2023; Published: Janaury 30, 2024

How to cite this article: Djibet Mbainguesse, Abakar Mahamat Seid, Bakari Abbo and Youssouf Paré, Hermite operational matrix and collocation methods for solving linear fractional Fredholm integro-differential equation, Far East Journal of Applied Mathematics 117(1) (2024), 1-18. http://dx.doi.org/10.17654/0972096024001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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