High-Precision Method for Space-Time-Fractional Klein-Gordon Equation

This paper presents the space-time fractional Klein-Gordon equations (FKGEs) for the spinless particle in potential field. It defines to describe the Higgs boson and the propagation of a boson in vacuum in Standard Model (SM). Besides, in this paper, the sine method is employed to construct exact solutions of the space-time fractional Klein-Gordon equations. Many new families of exact traveling wave solutions of the space-time fractional Klein-Gordon equations are successfully obtained. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.