Abstract
In this paper, the fractional Riccati method is modified for solving nonlinear variable coefficients fractional differential equations involving modified Riemann–Liouville derivative. This approach is successfully applied to the variable coefficient space–time fractional Korteweg de Vries (vcSTFKdV) equation. Variety of analytical solutions are obtained. The validity of this approach is discussed. The arbitrariness of the non-integer derivative order α possesses much richer structures. The amplitude increases when the non-integer derivative order increases such that 0.1<α⩽1. While it decreases the non-integer derivative order increases such that 0<α<0.1. From the graphical presentation of the obtained solutions it is observed that changing the non-integer derivative order value α affects the soliton behavior in a fundamental way; therefore, the non-integer derivative order can modify the wave shape without changing the properties of the medium, the nonlinearity and the dispersive effects.