A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations

[摘要] In this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system.

[关键词] Modified Riemann-Liouville derivative;Riccati-Bernoulli Sub-ODE method;exact solution;fractional Zoomeron equation;(3 + 1) dimensional space-time fractional mKDV-ZK equation