Fractional sub-equation method to space–time fractional Calogero-Degasperis and potential Kadomtsev-Petviashvili equations

Abstract

In the present paper, we construct the analytical solutions of some nonlinear equations involving Jumarie's modified Riemann-Liouville derivative in mathematical physics; namely the space–time fractional Calogero-Degasperis (CD) equation and the space–time fractional potential Kadomtsev-Petviashvili (PKP) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. This method is more powerful and will be used in further works to establish more entirely new solutions for other kind of nonlinear fractional PDEs arising in mathematical physics.

Keywords

• Fractional sub-equation method
• Fractional differential equation
• Modified Riemann-Liouville derivative
• Mittag-leffler function
• Analytical solutions