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In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space-time fractional generalized nonlinear Hirota-Satsuma coupled KdV equations, the spacetime fractional nonlinear Whitham-Broer-Kaup equations, the space-time fractional nonlinear coupled Burgers equations and the space-time fractional nonlinear coupled mKdV equations.ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

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New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.

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