Dispersion analysis and improved F-expansion method for space–time fractional differential equations

Abstract

In this article, an improved F-expansion method with the Riccati equation is suggested for space–time fractional differential equations for exact solutions. The fractional complex transformation is used to convert the space–time fractional differential equations into ordinary differential equations. The application of the method is described by solving space–time fractional potential Yu–Toda–Sasa–Fukuyama equation, and the solutions of the equation are successfully established in terms of the hyperbolic, trigonometric and rational types of functions. The graphical analysis describes the effect of fractional orders $$\alpha $$ , $$\beta $$ , $$\gamma $$ , $$\delta $$ of time and space derivatives, respectively, on the wave profile of solutions. The dispersion relation is obtained using the linear analysis, and it shows that waves follow anomalous or normal dispersion depending upon space or time fractional-order values.