New wave solutions for the fractional-order biological population model, time fractional burgers, Drinfel’d–Sokolov–Wilson and system of shallow water wave equations and their applications

Abstract In this research, by applying the improved -expansion method, we have found the travelling and solitary wave solutions of the fractional-order biological population model, time fractional Burgers equation, the Drinfel’d–Sokolov–Wilson equation and the system of shallow water wave equations. The advantage of this method is providing a new and more general travelling wave solutions for many non-linear evolution equations, it supply three different kind of solutions in the form (the hyperbolic functions, the trigonometric functions and the rational functions). This method included the extended -expansion method when and the -expansion method when N takes only positive value and zero. All of these merits help us in survey of the physical meaning of each models mentioned above for investigating stability of these models. Rapprochement between our results and the previous renowned outcome presented.

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