ABSTRACT
Numerous phenomena in physics and applied science have been described effectively by developing the models utilizing fractional calculus, which is also known as the theory of derivatives and integrals of non-integer order. This chapter describes new exact solutions of time-fractional coupled Drinfeld–Sokolov–Wilson equations by using a new reliable analytical method. It presents a comparatively new method, viz., the Jacobi elliptic function method for finding some new exact solutions of time-fractional coupled Drinfeld–Sokolov–Wilson equations. Analytical methods are devised to uniformly construct a series of exact solutions for general integrable and non-integrable non-linear evolution equations. The most essential interest of the newly proposed method is that it takes less computation for obtaining the exact solutions. The exact solutions obtained from the proposed method have also been used for presenting the numerical simulations. The proposed method is an effective and powerful technique for handling the fractional non-linear differential equation to obtain the explicit analytical solutions.
