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THERMAL SCIENCE
International Scientific Journal
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NEW EXACT SOLUTIONS OF THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL KADOMSTEV-PETVIASHVILI EQUATION
ABSTRACT
Aided by the local fractional derivative, we present a new local fractional (3+1)-dimensional Kadomstev-Petviashvili equation for describing the fractal water wave in this work. The non-differentiable transform is utilized to convert the local fractional equation into a local fractional ODE. On defining the Mittag-Leffler function on the Cantor sets, then a trial function based on the Mittag-Leffler function is proposed to seek for the non-differentiable exact solutions. The results reveal that the proposed method is a promising way to study the local fractional PDE arising in engineering and physics.
KEYWORDS
local fractional derivative, Mittag-Leffler function, trial function, Cantor sets, non-differentiable exact solutions
PAPER SUBMITTED: 2024-02-02
PAPER REVISED: 2024-03-11
PAPER ACCEPTED: 2024-05-09
PUBLISHED ONLINE: 2024-09-28
DOI REFERENCE: https://doi.org/10.2298/TSCI2404473D
CITATION EXPORT: view in browser or download as text file
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© 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