Traveling Wave Solutions of Some CFD Reaction Duffing and Diffusion–Reaction Equations Arising in Mathematical Physics

In this article, we developed exact solutions of the conformable fractional differential (CFD) generalized reaction Duffing model and conformable nonlinear fractional diffusion–reaction equation (Ö. Güner and A. Bekir in International Journal of Biomathematics 8:1550003, 2015). The duffing type equation is succeeded in explaining many different oscillations in different physical systems and diffusion–reaction equation describe the behavior of a large range of chemical systems. The modified \((G^{\prime } /G^{2} )\) $(G^{\prime }/G^2)$ -expansion method has been executed to solving fractional differential equation (FDEs). This method’s key advantage over others is that it provides more broad solutions with some free parameters. These models had applications in biology, fluid mechanics, bio-genetics, population dynamics, bio-mathematics, fractional dynamics, applied mathematics and physics. The suggested constraints conditions in the form of traveling wave transformations to convert CFD equations into the ODEs. The modified \((G^{\prime } /G^{2} )\) $(G^{\prime }/G^2)$ -expansion method is applied. As a consequence, some new bright, kink, bright-periodic and singular type of solutions are gained and are verified through MATHEMATICA. The mentioned method is more reliable, applicability and simple as compared to many other methods to solve conformable nonlinear FDEs.