Closed form solutions of nonlinear space‐time fractional Drinfel'd‐Sokolov‐Wilson equation via reliable methods

Abstract

In current study, the closed form solutions for nonlinear space‐time fractional Drinfel'd‐Sokolov‐Wilson (FDSW) equation are obtained in the presence of the beta derivatives and using reliable methods. Applying the (G′/G)‐expansion method, the hyperbolic, trigonometric, and rational function solutions of space‐time FDSW equation are derived. It is interesting to propose the generalized complex method to construct the closed form solutions of nonlinear fractional differential equations (NFDEs), and it is a good example to apply for searching exact solutions of space‐time FDSW equation. Computer simulations of solutions obtained via these two reliable methods are also presented by some figures with different values of the parameter beta. The results reveal that these two methods are efficient and direct approaches for solving various fractional differential equations in mathematical physics.