## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Periodic solution of fractal Phi-4 equation

**ABSTRACT**

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 nonlinearity. 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 to 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.

**KEYWORDS**

PAPER SUBMITTED: 2020-05-02

PAPER REVISED: 2020-05-31

PAPER ACCEPTED: 2020-05-31

PUBLISHED ONLINE: 2021-01-31

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