Exact Solutions for Time-Fractional Ramani and Jimbo—Miwa Equations by Direct Algebraic Method

Abstract

In this study, the analytical solutions of some nonlinear time-fractional partial differential equations are investigated by the direct algebraic method. The nonlinear fractional partial differential equation (NLfPDE) which is based on the fractional derivative (fd) in the sense of modified Riemann-Liouville derivative is transformed to the nonlinear non-fractional ordinary differential equation. The hyperbolic and rational functions which are contained solutions are obtained for the sixth-order time-fractional Ramani equation and time-fractional Jimbo—Miwa equation (JME) with the help of this technique. In addition, this method can be applied to higher order and higher dimensional NLfPDEs. Finally, three dimensional simulations of some solutions are given.