A class of computational approaches for simulating fractional functional differential equations via Dickson polynomials

Abstract

In this paper, a new class of computational techniques for the numerical solution of fractional functional differential equations is discussed. The proposed technique is based on Dickson polynomials with which well-known polynomials such as Fibonacci, Lucas and Chebyshev polynomials are related with some parameters. In general, the proposed combined scheme is improved by the fractional Dickson-Tau collocation technique in which a Dickson operation matrix is constructed for fractional differentiation. Then, a genetic algorithm is used to tune the unknown parameters of the proposed methods. Moreover, the error estimates and convergence of the proposed scheme are analysed. The significance of the accuracy and low computational time of the proposed scheme is verified in several numerical examples.