A new analytical approach to solve some of the fractional-order partial differential equations

Abstract

The aim of the present paper is to present an analytical method for the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations by using the generalized tanh–coth method. The fractional derivative is described in the sense of the modified Riemann–Liouville derivatives. The method gives an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. We have obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these fractional equations to ordinary differential equations which subsequently resulted into number of exact solutions.