Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method

Abstract

In this paper, our focus is on the multidimensional mathematical physics models. We employ the sub-equation method to obtain new exact solutions to the proposed strongly nonlinear time-fractional differential equations of conformable type. The models considered are generalized Benjamin equation, modified generalized multidimensional Kadomtsev–Petviashvili (KP) equations, modified generalized multidimensional KP–BBM equation and the variant Boussinesq system of equations. We also introduced a new modified generalized multidimensional KP type equation and its exact solutions. As the order of fractional derivative tends to one, the obtain exact solutions by the proposed method reduce to classical solutions. We successfully established varieties of soliton type solutions. The results obtained affirm that sub-equation method is an efficient and powerful technique for analytic solutions of nonlinear fractional partial differential equations.