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

A. M. S. Mahdy a,* and A. A. A. Al-Emamb

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

Authors :

A. M. S. Mahdy ^a,* and A. A. A. Al-Emam^b

Author Address :

^a,b Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

*Corresponding author

Abstract :

In this paper, we use shifted Chebyshev approximations with the second kind \cite{Swe5} and fractional power series method (FPSM) (\cite{Cui}, \cite{El-Ajou}) 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 with the traditional methods \cite{Swe1}.

Keywords :

Shifted Chebyshev polynomials with the second kind; Fractional power series method; Caputo derivative; Multi-order nonlinear fractional differential equations.

DOI :

Article Info :

Received : July 07, 2016; Accepted : December 23, 2016.