TY - JOUR
TI - Dynamic behaviors of the non-linear local fractional heat conduction equation on the cantor sets
AU - Li Geng
AU - Wang Kang-Jia
JN - Thermal Science
PY - 2024
VL - 28
IS - 4
SP - 3391
EP - 3396
PT - Article
AB - 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.