Thermal Science

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Caixia Liu

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 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.

KEYWORDS

fractal calculus, periodic solution, solitary wave, two-scale mathematics, Duffing oscillator

PAPER SUBMITTED: 2020-05-02

PAPER REVISED: 2020-05-31

PAPER ACCEPTED: 2020-05-31

PUBLISHED ONLINE: 2021-01-31

DOI REFERENCE: https://doi.org/10.2298/TSCI200502032L

CITATION EXPORT: view in browser or download as text file

THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE No. 2, PAGES [1345 - 1350]

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Periodic solution of fractal Phi-4 equation

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence