A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order gamma in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Keywords:

Chebyshev polynomials , orthogonal system , fractional differential equation , fractional-order Chebyshev functions , Operational matrix