HERMITE OPERATIONAL MATRIX AND COLLOCATION METHODS FOR SOLVING LINEAR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
Keywords:
fractional derivative in sense of Caputo, fractional Fredholm integro-differential equation, Hermite operation matrix.DOI:
https://doi.org/10.17654/0972096024001Abstract
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.
Received: October 18, 2023
Accepted: November 6, 2023
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