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

Abstract

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-Le er function, where, the rst fractional orderis included in the power law function and the second fractional order is thegeneralized Mittag-Le er 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.