Paper Title
Numerical Solutions of Fractional Differential Equations using Shifted Chebyshev Polynomials of the Fourth Kind

Abstract
In this paper a numerical solution for the fractional-order Bagley-Torvik differential equations using Shifted Chebyshev polynomials of the fourth kind is proposed. Shifted Chebyshev polynomials of the fourth kind approximate the fractional differential equation with a system of algebraic equations. The solution of those algebraic equations provides the coefficient vector c, which, in turn yields the numerical solution of the fractional-order Bagley-Torvik differential equation. Numerical example results demonstrate that the numerical solution is a very accurate approximation to the FDE. Keywords - Shifted Chebyshev Polynomials of the Fourth Kind, Collocation Method, Fractional Differential Equations, Numerical FDE Solutions.