4.3 Article

NON-DIFFERENTIABLE SOLUTIONS FOR NON-LINEAR LOCAL FRACTIONAL HEAT CONDUCTION EQUATION

期刊

THERMAL SCIENCE
卷 25, 期 -, 页码 S309-S314

出版社

VINCA INST NUCLEAR SCI
DOI: 10.2298/TSCI21S2309Z

关键词

non-differentiable solution; fractional calculus; Painleve analysis; local fractional heat conduction equation; Backlund transformation

资金

  1. Liaoning BaiQianWan Talents Program of China
  2. Natural Science Foundation of Education Department of Liaoning Province of China [LJ2020002]

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This paper investigates a (2+1)-dimensional local fractional heat conduction equation with arbitrary non-linearity, constructs a Backlund transformation, and obtains exact non-differentiable solutions showing spatio-temporal fractal structures. Fractional calculus is shown to play a crucial role in handling non-differentiable problems.
Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation of a reduced form of the local fractional heat conduction equation is constructed by Painleve analysis. Based on the Backlund transformation, some exact non-differentiable solutions of the local fractional heat conduction equation are obtained. To gain more insights of the obtained solutions, two solutions are constrained to a Cantor set and then two spatio-temporal fractal structures with profiles of these two solutions are shown. This paper further reveals by local fractional heat conduction equation that fractional calculus plays important role in dealing with non-differentiable problems.

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