GENERAL FRACTIONAL CALCULUS IN NON-SINGULAR POWER-LAW KERNEL APPLIED TO MODEL ANOMALOUS DIFFUSION PHENOMENA IN HEAT TRANSFER PROBLEMS

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.