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Apr 27, 2017
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Jun 1, 2014
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Abstract

In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve  certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The  results obtained reveal that these  methods are  both very effective and simple for finding approximate solutions. Some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods.

 

 

Keywords

Homotopy perturbation Fractional differential equation Shallow water equations Approximate solutions.

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References

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