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.