Abstract
In this article, we acquire a variety of new exact traveling wave solutions in the form of trigonometric, hyperbolic, and rational functions for the nonlinear time-fractional Clannish Random Walker's Parabolic (CRWP) equation in the sense of beta-derivative by employing the two modified methods, namely, modified (G' /G(2)) - expansion method and modified F- expansion method. The obtained solutions are verified for aforesaid equations through symbolic soft computations. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions. The obtained solutions show that the presented methods are effective, straight forward, and reliable as compared to other methods. These methods can also be used to extract the novel exact traveling wave solutions for solving any types of integer and fractional differential equations arising in mathematical physics.