American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2013, 1(1), 14-19
DOI: 10.12691/ajma-1-1-3
Open AccessArticle

The Fractional Sub-Equation Method and Exact Analytical Solutions for Some Nonlinear Fractional PDEs

J. F. Alzaidy1,

1Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia

Pub. Date: February 26, 2013

Cite this paper:
J. F. Alzaidy. The Fractional Sub-Equation Method and Exact Analytical Solutions for Some Nonlinear Fractional PDEs. American Journal of Mathematical Analysis. 2013; 1(1):14-19. doi: 10.12691/ajma-1-1-3

Abstract

In the present paper, a fractional sub-equation method is proposed to solve fractional differential equations. Being concise and straightforward, this method is applied the space–time fractional Potential Kadomtsev–Petviashvili (PKP) equation and the space–time fractional Symmetric Regularized Long Wave (SRLW) equation. As a result, many exact analytical solutions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear fractional PDEs arising in mathematical physics.

Keywords:
fractional sub-equation method fractional differential equation modified Riemann–Liouville derivative Mittag-Leffler function analytical solutions

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