Numerical solutions of Fourier's law involving fractional derivatives with bi-order

Document Type: Article

Authors

1 CONACyT-Centro Nacional de Investigacion y Desarrollo Tecnologico. Tecnologico Nacional de Mexico

2 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences. University of the Free State, Bloemfontein 9300, South Africa.

3 Centro Nacional de Investigacion y Desarrollo Tecnologico.Tecnologico Nacional de Mexico

Abstract

In this paper, we present an alternative representation of the fractional spacetime
Fourier's law equation using the concept of derivative with two fractional
orders and . The new de nitions are based on the concept of power law
and the generalized Mittag-Leer function, where, the rst fractional order
is included in the power law function and the second fractional order is the
generalized Mittag-Leer function. The new approach is capable of considering
media with two di erent layers, scales and properties. The generalization of
this equation exhibit di erent cases of anomalous behavior and Non-Fourier
heat conduction processes. Numerical solutions using an iterative scheme were
obtained.

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