Abstract
In this paper, we obtain the exact traveling solutions of the M-fractional generalized reaction Duffing model and density dependent M-fractional diffusion reaction equation by using three fertile, (G'/G, 1/G), modified (G'/G(2)) and (1/G')-expansion methods. These methods contribute a variety of exact traveling wave solutions to the scientific literature. The obtained solutions are also verified for the aforesaid equations through symbolic soft computations. Furthermore, some results are explained through numerical simulations that show the novelty of our work. Moreover, we observe that all the solutions are new and an excellent contribution in the existing literature of solitary wave theory.