Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches

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.

Automated summary

In this paper, exact traveling wave solutions of the M-fractional generalized reaction Duffing model and density dependent M-fractional diffusion reaction equation are obtained using three fertile expansion methods ((G'/G, 1/G), modified G'/G(2) and 1/G'). These solutions are validated through symbolic soft computations and supported by numerical simulations. The novelty and contribution of the new solutions to the existing literature of solitary wave theory are also highlighted.