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

•M−fractional derivative is used for the modeled the reaction Duffing model and diffusion–reaction equation.•Exact traveling solutions of the M−fractional generalized reaction Duffing model and density dependent M−fractional diffusion reaction equation by using three fecund, G′/G,1/G, modified G′/G2 and 1/G′-expansion methods.•The obtained solutions verify the all obtained solutions. Also some of the obtained solutions are explained through numerical simulations.•The obtained solutions are new and an excellent contribution in the existing scientific literature. 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′/G2 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.