Open AccessPeriodic solution of fractal Phi-4 equation
Author(s) -
Caixia Liu
Publication year - 2021
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci200502032l
Subject(s) - fractal , fractal derivative , property (philosophy) , mathematical analysis , differential equation , space (punctuation) , scale (ratio) , physics , fractal dimension , mathematics , fractal analysis , computer science , quantum mechanics , philosophy , epistemology , operating system
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.