Second kind shifted Chebyshev polynomials and power series method for solving multi-order non-linear fractional differential equations

Abstract

In this paper, we use shifted Chebyshev approximations with the second kind [25] and fractional power series method (FPSM) ([3], [8]) to solve the multi-order non-linear fractional differential equations. The fractional derivative is described in the Caputo sense. The properties of shifted Chebyshev polynomials with the second kind are utilized to reduce multi-order NFDEs. The system of non-linear of algebraic equations which solved by using Newton iteration method. We compared with FPSM. The results are compared withthe traditional methods [23].