A Collocation Technique based on an Orthogonal Polynomial for Solving Malti-Order Fractional Integro-differential Equations.

Abstract

This paper deals with construction of orthogonal polynomial functions and the application of same to solve multi-order fractional integro – differential equations. The method used in the equation is referred to as the standard collation method. The method assumes an approximate solution in which the constructed orthogonal polynomials are used as basis functions. The assumed solution is substituted into the general class of multi- order fractional integro- differential equations and the resulting equation is then collocated at equally spaced interior points, thus resulting in algebraic linear system of equations which are to be solved by Gaussian elimination method in order to obtain the unknown constants in the assumed solution. Some numerical examples are presented to illustrate the validity and applicability of the method. The results obtained using the method is shown on tables of results.