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

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 α and β. The new definitions are based on the concept of power law and the generalized Mittag-Leffer function, where the first fractional order is incorporated into the power law function, and the second fractional order is the generalized Mittag-Leffer function. The new approach is capable of considering media with two different layers, scales, and properties. The generalization of this equation exhibits different cases of anomalous behaviors and Non-Fourier heat conduction processes. Numerical solutions are obtained using an iterative scheme.