THERMAL SCIENCE

International Scientific Journal

Geng Li

,

Kang-Jia WangORCID

DYNAMIC BEHAVIORS OF THE NON-LINEAR LOCAL FRACTIONAL HEAT CONDUCTION EQUATION ON THE CANTOR SETS

ABSTRACT
Based on the local fractional derivative, a fractal non-linear heat conduction equation, which can model the behavior of the heat transfer in the fractal medium, is extracted in this work. On defining the Mittag-Leffler function on the Cantor sets, two special functions namely the THυ(μυ) function and CHυ(μυ) function are constructed, and then are employed along with Yang's non-differentiable transfor­mation seek for the non-differentiable exact solutions. The obtained results confirm that the proposed method iseffective and powerful, and can provide a promising way to find the exact solutions of the fractal PDE.
KEYWORDS
local fractional derivative, Mittag-Leffler function, Cantor sets, Yang’s non-differentiable transformation, special functions
PAPER SUBMITTED: 2024-02-22
PAPER REVISED: 2024-03-29
PAPER ACCEPTED: 2024-05-09
PUBLISHED ONLINE: 2024-09-28
DOI REFERENCE: https://doi.org/10.2298/TSCI2404391L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE No. 4, PAGES [3391 - 3396]
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Dynamic behaviors of the non-linear local fractional heat conduction equation on the cantor sets

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