Communications in Theoretical Physics ›› 2020, Vol. 72 ›› Issue (5): 055003. doi: 10.1088/1572-9494/ab7707

• Mathematical Physics • Previous Articles     Next Articles

Analytical and approximate solutions of (2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

Mehmet Senol()   

  1. Department of Mathematics, Nevsehir Haci Bektas Veli University, Nevsehir, Turkey
  • Received: 2019-12-11 Revised: 2020-02-06 Accepted: 2020-02-16 Published: 2020-05-01

Abstract:

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely Burgers-Kadomtsev-Petviashvili equation (Burgers-K-P) that arises in shallow water waves. Furthermore, using the residual power series method (RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.

Key words: fractional partial differential equations, Burgers-Kadomtsev-Petviashvili equation, conformable fractional derivative, sub-equation method, residual power series method