IJPAM: Volume 109, No. 3 (2016)

SOLITARY SOLUTION OF A CLASS OF NONLINEAR
TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

H. Parsian$^1$, R. Sabzpoushan$^2$
$^1$Department of Physics
Bu-Ali Sina University
Hamadan, IRAN
$^2$Department of Electrical Engineering
Bu-Ali Sina University
Hamadan, IRAN

Abstract. This paper presents a general solitary solution of a class of nonlinear time-fractional partial differential equations by Adomian decomposition method(ADM). This class of nonlinear time-fractional partial differential equations include a lot of standard nonlinear partial differential equations in mathematical physics. The solitary solution obtained by ADM is a general solitary solution and admit you investigate the solution for different initial conditions and different $\alpha$( $\alpha$ is the order of derivative respect to time $0< \alpha \le 1$). Also the solution subject to the especial initial conditions and $\alpha=1$ reduce to the solution of standard partial differential equation. Additionally, it use the fractional derivative of Caputo sense.

Received: April 13, 2016

Revised: July 19, 2016

Published: October 1, 2016

AMS Subject Classification: 34A08, 76B25, 65M55

Key Words and Phrases: fractional differential equation, solitary wave, Adomian decomposition method
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DOI: 10.12732/ijpam.v109i3.22 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 757 - 762


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