Searching closed form analytic solutions to some nonlinear fractional wave equations

Abstract

Numerous tangible incidents in physics, chemistry, applied mathematics and engineering are described successfully by means of models making use of the theory of derivatives of fractional order and research in this area has grown significantly. In this article, we establish exact solutions to some nonlinear fractional differential equations. The recently established rational ()-expansion method with the help of fractional complex transform is used to examine abundant further general and new closed form wave solutions to the nonlinear space-time fractional mBBM equation, the space-time fractional Burger’s equation and the space-time fractional ZKBBM in the sense of the Jumarie modified Riemann-Liouville derivative. The fractional complex transform reduces the nonlinear fractional differential equations into nonlinear ordinary differential equations and then the theories of ordinary differential equations are implemented effectively. It is observed that the performance of this method is reliable, useful and gives new and broad-ranging closed form solutions than the existing methods.

Keywords

• exact solutions
• modified riemann-liouville derivative
• nonlinear fractional complex transformation
• nonlinear space-time fractional pdes