## Solitary wave solutions for a time-fraction generalized hirota-satsuma coupled KdV equation by an analytical technique.(English)Zbl 1205.35251

Summary: We implement a relatively analytical technique, the homotopy perturbation method (HPM), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo derivatives. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. He’s homotopy perturbation method (HPM) which does not need small parameter is implemented for solving the differential equations. It is predicted that HPM can be found widely applicable in engineering.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 26A33 Fractional derivatives and integrals 35Q51 Soliton equations

### Keywords:

homotopy perturbation method; Caputo derivative
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### References:

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