A numerical solution of variable order fractional functional differential equation based on the shifted Legendre polynomials

Abstract

This paper deals with the numerical approach of a class of variable order fractional functional boundary value problems. The fractional derivative is described in the variable order Caputo sense. The method is based upon shifted Legendre polynomials. The properties of shifted Legendre polynomials are utilized to reduce the given fractional differential equation problem to the system of algebraic equations. To show the performance of the method some numerical examples are provided and the results are compared with two other methods.