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.