ABSTRACT
In the chapter 7, the solitary wave exact solutions of non-linear evolution equations, namely, time-fractional fifth-order Sawada-Kotera, time-fractional fifth-order modified Sawada-Kotera, time-fractional fifth-order Kuramoto-Sivashinsky (K-S) equations, and fractional coupled Jaulent-Miodek equation have been determined by the newly proposed tanh-sech method via fractional complex transform. Also, the Kudryashov method has been applied to solve the time-fractional fifth-order mS-K equation. By applying the tanh-sech method; three solitary wave solutions have been obtained. Both methods provide new and more general type solitary wave solutions which are significant to reveal the pertinent features of the physical phenomenon. The fractional complex transform can easily convert a fractional differential equation into its equivalent ordinary differential equation form. By using the obtained solutions, the three-dimensional graphs have been drawn, which give the nature of the solutions as solitary wave.
