Exact and solitary wave solutions of conformable time fractional Clannish Random Walker’s Parabolic and Ablowitz-Kaup-Newell-Segur equations via modified mathematical methods

Abstract

The nonlinear fractional differential equations (FDEs) composed by mathematical modeling through nonlinear corporeal structures. The study of these kind models has an energetic position in different field of applied sciences. The dominant intension of this article is to extract novel analytical wave solutions of the conformable time fractional Clannish Random Walker’s Parabolic (CRWP) and (2 + 1)-dimensional fractional Ablowitz-Kaup-Newell-Segur (AKNS) equations in the sense of conformable derivative with the aid of modified mathematical methods, called modified extended auxiliary equation mapping and modified F-expansion schemes. By the virtue of employed techniques, different types of solutions are obtained in the form of trigonometric, hyperbolic, exponential and rational functions respectively. To prompt the essential propagated features, some investigated solutions are exhibited in form of 3D and 2D is planned by passing on the precise values to the parameters under the constrain conditions. The accomplished solutions show that these presented schemes are reliable, applicable and efficient.