Closed-form solutions to the conformable space-time fractional simplified MCH equation and time fractional Phi-4 equation

The time-fractional problem is a class of important models to represent the real phenomena. We construct new solitary waves for the space-time fractional simplified modified Camassa-Holm (MCH) and the time fractional Phi-4 equations using the unified solver. The fractional derivatives are defined in the sense of the new con-formable fractional derivative. The acquired solutions may be useful for various vital observations in nuclear and particle physics and fluid mechanics. The proposed unified solver is a sturdy mathematical tool for solving various classes of fractional partial differential equations in applied science. Moreover, the simulation of some selected solutions has been demonstrated with the aid of matlab software.