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British Journal of Mathematics & Computer Science

British Journal of Mathematics & Computer Science, ISSN: 2231-0851,Vol.: 3, Issue.: 2 (April-June)


Original Research Article


Fractional Sub-Equation Method and its Applications to the Space–Time Fractional Differential Equations in Mathematical Physics



J. F. Alzaidy1*

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




In the present paper, we construct the analytical solutions of some nonlinear evolution equations involving Jumarie’s modified Riemann–Liouville derivative in mathematical physics; namely the space–time fractional modified Benjamin-Bona-Mahony(mBBM) equation and the space–time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony(ZKBBM) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. 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.



DOI : 10.9734/BJMCS/2013/2908

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