Analytical solutions to the nonlinear space–time fractional models via the extended $$\left( {\frac{{G^{\prime } }}{{G^{2} }}} \right)$$-expansion method

Abstract

Based on the extended $$\left(\frac{G^{'}}{G^2}\right)$$ -expansion method, the nonlinear space–time fractional $$(3 + 1)$$ -dimensional Jimbo–Miwa and the nonlinear space–time fractional Korteweg–de Vries–Burgers equations are studied. Many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. These solutions characterize numerous physical meanings such as solitary wave solutions, soliton wave solutions, periodic wave solutions, and complex function solutions. The corresponding plots of some of the obtained solitary wave solutions are given out graphically.