PERIODIC SOLUTION OF FRACTAL PHI-4 EQUATION

This paper focuses on a fractal Phi-4 equation with time-space fractal derivatives, though its solitary solutions have been deeply studied, its periodic solution was rarely revealed due to its strong non-linearity. Now the condition is completely changed, He's frequency formulation provides with a universal tool to having a deep insight into the periodic property of the fractal Phi-4 equation. The two-scale transform is used to convert approximately the fractal Phi-4 equation a differential model, and a criterion is suggested for the existence of a periodic solution of the equation, the effect of fractal orders on the periodic property is also elucidated.

Automated summary

This paper investigates the periodic solution of a fractal Phi-4 equation, utilizing He's frequency formulation and two-scale transform to propose a criterion for determining the existence of periodic solutions, and elucidating the impact of fractal orders on periodic properties.