Abstract
We construct new solitary structures for time fractional Phi-4 and space-time fractional simplified modified Camassa-Holm (MCH) equations, utilizing the unified solver technique. The time (space-time) fractional derivatives are defined via sense of the new conformable fractional derivative. The unified solver technique extract vital solutions in explicit way. The obtained solutions may be beneficial for explaining many complex phenomena arising in fluid mechanics, nuclear, plasma and particle physics. The unified solver method is a vital tool for handling further models arising in applied science and new physics. For detailed physical dynamical representation of our results, 3D and 2D profiles to some of the gained solutions are also illustrated using Matlab software.