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.
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