NUMERICAL APPROXIMATION OF SINGULAR MULTI-ORDER FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS BY LEAST SQUARES AND AKBARI-GANJI'S METHODS

O. A.  Uwaheren; Opeyemi  Odetunde; E. O.  Anyanwu; F. Y.  Aderibigbe; C. L.  Pius

O. A. Uwaheren Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.
Opeyemi Odetunde Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.
E. O. Anyanwu Department of Mathematics, Alvan Ikoku University of Education, Owerri, Imo State, Nigeria.
F. Y. Aderibigbe Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.
C. L. Pius Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.

Keywords: Singular Multi-order Fractional, Volterra Integro-differential Equations, Least Squares Method, Akbari-Ganji's Method

Abstract

This article is concerned with the numerical solution of singular multi-order fractional Volterra integro-dierential equations. Two numerical methods are proposed; Least Squares and Akbari-Ganji's Methods using Legendre polynomials as basis functions. The proposed methods were demonstrated on some examples to verify their practicability and the results obtained were very close to the exact solution.

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