Exact solutions to conformable time-fractional Klein–Gordon equation with high-order nonlinearities

Abstract

In this paper, we solve the conformal time-fractional Klein–Gordon equation with high-order nonlinearities via the complete discrimination system for polynomial method, namely with the quadratic and cubic nonlinearities. Our results contain all the existing solutions, and some new exact solutions such as Jacobian elliptic function solutions, are also presented. Moreover, to ensure the existence of each solution, the concrete examples are given and the discussions of the influence of the fractional order are also presented.

Keywords

• Time-fractional Klein–Gordon equation
• Complete discrimination system for polynomial method
• Conformal fractional derivative
• Quadratic and cubic nonlinearities
• Exact solutions