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General fractional calculus in non-singular power-law kernel applied to model anomalous diffusion phenomena in heat transfer problems

Gao Feng (China University of Mining and Technology, State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou, China + China University of Mining and Technology, School of Mechanics and Civil Engineering, Xuzhou, China)

In this paper we address the general fractional calculus of Liouville-Weyl and Liouville-Caputo general fractional derivative types with non-singular power-law kernel for the first time. The Fourier transforms and the anomalous diffusions are discussed in detail. The formulations are adopted to describe complex phenomena of the heat transfer problems.

Keywords: heat transfer, anomalous diffusion, general fractional calculus, Fourier transforms