Solitary and periodic wave solutions to the family of nonlinear conformable fractional Boussinesq‐like equations

Abstract

The current study investigates the exact solitary, singular, and periodic singular wave solutions to the family of nonlinear fractional Boussinesq‐like (Bq‐like) equations using the (G′/G,1/G)‐expansion method. The considered equations in the sense of conformable derivative are converted into ordinary differential equations with the assist of fractional transformation. Applying the (G′/G,1/G)‐expansion method through the symbolic computation package Maple, some new exact solitary, singular, and periodic wave solutions to the considered equations in fractional forms are acquired in terms of a variety of complex hyperbolic, trigonometric, and rational functions. Moreover, the particular solutions extracted by the mentioned method are expressed with the combination of tanh, sech; coth, csch; tan, sec, and cot, csc functions. Among the produced solutions, some of the new solutions have been visualized by three‐dimensional (3D) and two‐dimensional (2D) graphics under the choice of suitable arbitrary parameters to show their physical interpretation. The acquired results demonstrate the power of the executed method to evaluate the exact solutions of the nonlinear fractional Bq‐like equations, which may be used for applying nonlinear water model to coastal and ocean engineering. All the produced solutions have been verified by substituting back into their corresponding equations with the aid of symbolic computation software Maple 17.