Abundant Explicit Solutions to Fractional Order Nonlinear Evolution Equations

We utilize the modified Riemann–Liouville derivative sense to develop careful arrangements of time-fractional simplified modified Camassa–Holm (MCH) equations and generalized (3 + 1)-dimensional time-fractional Camassa–Holm–Kadomtsev–Petviashvili (gCH-KP) through the potential double - expansion method (DEM). The mentioned equations describe the role of dispersion in the formation of patterns in liquid drops ensued in plasma physics, optical fibers, fluid flow, fission and fusion phenomena, acoustics, control theory, viscoelasticity, and so on. A generalized fractional complex transformation is appropriately used to change this equation to an ordinary differential equation; thus, many precise logical arrangements are acquired with all the freer parameters. At the point when these free parameters are taken as specific values, the traveling wave solutions are transformed into solitary wave solutions expressed by the hyperbolic, the trigonometric, and the rational functions. The physical significance of the obtained solutions for the definite values of the associated parameters is analyzed graphically with 2D, 3D, and contour format. Scores of solitary wave solutions are obtained such as kink type, periodic wave, singular kink, dark solitons, bright-dark solitons, and some other solitary wave solutions. It is clear to scrutinize that the suggested scheme is a reliable, competent, and straightforward mathematical tool to discover closed form traveling wave solutions.