optical solitary solution of two coupled fractional equations with new modification of exp function method

In past years, various methods were applied to achieve the analytical solution of the fractional partial differential equation (fpde). however, most have not been applied directly to manipulate the system of equations. in the current paper, the modified exp function method is expanded to attain the answer of a fractional two-dimensional system, without reducing fractional equations. furthermore, the proposed methods have been used to achieve the analytical solutions of the coupled space time-fractional boussinesq-burgers system and coupled time-fractional long system. the proposed methods are highly accurate, flexible, effective, and programmable to solve nonlinear evolution equations. moreover, the plots of obtained solutions have been illustrated for some parameters.