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

Amr M. S. Mahdy; Ali A. A. El-dahdouh

doi:10.26637/mjm501/003

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 with
the traditional methods [23].

Keywords:

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

Mathematics Subject Classification:

65N20, 41D15

Authors Imprint References Funding Related Articles Downloads

Amr M. S. Mahdy Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.
Ali A. A. El-dahdouh Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

Pages: 19-28
Date Published: 01-01-2017
Vol. 5 No. 01 (2017): Malaya Journal of Matematik (MJM)

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