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

نویسندگان
Atangana, Abdon ID 1
Gomez-Aguilar, J.F. ID 2
Escobar-Jimenez, R.F. ID 3

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

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

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

doi
10.24200/sci.2017.4342
چکیده

In this paper, we present an alternative representation of the fractional spacetimeFourier's law equation using the concept of derivative with two fractionalorders and . The new de nitions are based on the concept of power lawand the generalized Mittag-Leer function, where, the rst fractional orderis included in the power law function and the second fractional order is thegeneralized Mittag-Leer function. The new approach is capable of consideringmedia with two di erent layers, scales and properties. The generalization ofthis equation exhibit di erent cases of anomalous behavior and Non-Fourierheat conduction processes. Numerical solutions using an iterative scheme wereobtained.

کلیدواژه‌ها
Anomalous difiusion, Fractional heat transfer model, Iterative Method, Bi-order fractional derivative, Non-Fourier heat conduction