The paper considers a nonlinear fractional integro-differential equation of Fredholm second kind. The approximate solution of this equation is computed using Laguerre orthogonal polynomial methods. The Caputo fractional derivatives and the integral in the equation can be converted into matricial and vectorial forms. By doing so, the original equation is transformed into a system of nonlinear algebraic equations, based on the points of collocation. Solving this system with the multivariate Newton’s iterative method is produced unknown coefficients in the expansion of Laguerre’s polynomials. The results show that the approximation method using Laguerre polynomials is accurate and efficient for solving fractional integro-differential of Fredholm of second kind.

nonlinear fractional integro-differential equation of Fredholm, Laguerre approximation technique, Caputo fractional derivative, multivariate Newton method.

Received: December 15, 2022; Accepted: March 14, 2023; Published: April 15, 2023

How to cite this article: Djibet Mbainguessé, Bakari Abbo and Youssouf Paré, Solving nonlinear fractional integro-differential equation of Fredholm second kind by an approximation technique of Laguerre polynomials and Newton iteration method, Universal Journal of Mathematics and Mathematical Sciences 19(1) (2023), 1-19. http://dx.doi.org/10.17654/2277141723014

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

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