Construction of Orthogonal Polynomial as Basis Function for Solving Fractional Order Integro Differential Equations

Abstract

This article is concerned with the use of orthogonal polynomials as basis functions to solve fractional order Integro-differential equations. Standard collocation method was used. We constructed orthogonal polynomials by assuming a quadratic weight function that is positive in the interval of consideration; [0, 1]. The assumed approximate function was substituted into the general class of fractional order Integro-differential equations and after some simplifications; the resulted equation was then collocated at equally spaced interior points of the interval. The resulted system of algebraic equations is solved to obtain the unknown constants. The constants are substituted back into the assumed approximate solution to get the required approximate solution.