Numerical solution of fractional differential equations using fractional Chebyshev polynomials

Abstract

In this paper, fractional order Chebyshev polynomials are presented and some properties are given. Using definition of fractional order Chebyshev polynomials, we give a numerical scheme for solving fractional differential equation by the collocation method. The Collocation method converts the given fractional differential equation into a matrix equation, which yields a linear algebraic system. Bagley-Torvik equation and fractional relaxation-oscillation equation are solved to show the effectiveness of the given method. This method is compared with some known schemes