Reduction of Order Method for Solving Some Time-Fractional Differential Equations

Abstract

The fractional derivative is considered in modified Riemann-Liouville derivative sense. A reduction of order method is used for constructing exact solution of some time fractional differential equations. More new soliton solution is obtained for time-fractional Klein-Gordon equation, time-fractional Burgers equation and time-fractional Hirota-Satsuma coupled KdV system. This method can be applied to many other nonlinear fractional partial differential equations in mathematical physics.

Keywords:Modified Riman-Liouville derivative, time-fractional Klein-Gordon equation, time-fractional Burgers equation and time-fractional Hirota-Satsuma coupled KdV system