PERIODIC SOLUTION OF FRACTAL PHI-4 EQUATION

被引：24
作者：
Liu, Caixia [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing, Peoples R China
来源：
THERMAL SCIENCE | 2021年 / 25卷 / 02期
关键词：
fractal calculus; periodic solution; solitary wave; Duffing oscillator; two-scale mathematics; FREQUENCY-AMPLITUDE FORMULATION; CALCULUS; MODEL;
D O I：
10.2298/TSCI200502032L
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
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.
引用
收藏
页码：1345 / 1350
页数：6
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