THERMAL SCIENCE

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Yi Tian

ITERATIVE SOLUTION FOR A CLASS OF PARTIAL DIFFERENTIAL EQUATIONS IN FRACTAL SPACES

ABSTRACT
A class of fractal PDE is successfully established by He's fractal derivative in a fractal space, and their variational principles are obtained by the semi-inverse method. The Fourier-Rabbani-He method and the Ritz-like method are used to solve the given fractal equations with initial value conditions. The example is a great demonstration of how the Fourier-Rabbani-He method is a powerful and simple tool that can be used in different ways.
KEYWORDS
Fourier-Rabbani-He Method, semi-inverse transform method, variational principle
PAPER SUBMITTED: 2024-03-05
PAPER REVISED: 2024-06-01
PAPER ACCEPTED: 2024-06-02
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503821T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1821 - 1828]
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Iterative solution for a class of partial differential equations in fractal spaces

2025 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