TY - JOUR
TI - Periodic solution of fractal Phi-4 equation
AU - Liu Caixia
JN - Thermal Science
PY - 2021
VL - 25
IS - 2
SP - 1345
EP - 1350
PT - Article
AB - 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.