Application of $$\tan (\Phi (\xi )/2)$$tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model

Abstract

Based on the $$\tan (\Phi (\xi )/2)$$-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.