Abstract
•Nonlinear analysis approach is used to solve the physical models.•The conformable time-fractional NFPDEs is studied.•Applying the robust solver to the nonlinear NFPDEs.•Highly performance and effcient of the proposed solver.•Obtaining some new solutions of the NFPDEs.
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 conformable 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.