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I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering,Academic Press, San Diego, Calif, USA, 1999.

has been cited by the following article:

Article

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

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


American Journal of Mathematical Analysis. 2013, Vol. 1 No. 1, 14-19
DOI: 10.12691/ajma-1-1-3
Copyright © 2013 Science and Education Publishing

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.

Correspondence to: J. F. Alzaidy, Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia. Email: Corresponding author: j-f-h-z @hotmail.com

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.

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