A Generalizing of the Fractional Sub-Equation Method to Solve Systems of the Space-Time Fractional Differential Equation

Abstract

In the present paper, we construct the analytical solutions of some Space-Time nonlinear fractional order systems involving Jumarie's modified Riemann-Liouville derivative in mathematical physics : such that Space-Time fractional Whitham-Broer-Kaup equations, Space-Time fractional Breaking Soliton equations, Space-Time fractional Coupled Boussinesq- Burgers equations and Space-Time fractional Coupled Burgers Equations by using The fractional sub-equation method . this method  is very powerful mathematical technique for finding exact solutions of nonlinear ordinary differential equations.

Key words: fractional sub-equation method, modified Riemann-Liouville derivative, Mittage-Leffler function.