Numerical Approximation of Atangana-Baleanu Caputo Fractional Derivative and Its Application to Fractional Order Subdiffusion Bioheat Equation

To address the limitations of the classical fractional derivative, which uses a local and singular kernel, Caputo and Fabrizio recently introduced a new fractional derivative with a non-local and non-singular exponential kernel. Atangana and Baleanu further generalized this derivative using the Mittag-Leffler function. In this paper, we apply the Atangana-Baleanu-Caputo fractional derivative to develop a fractional-order finite difference scheme for solving the fractional-order subdiffusion bioheat equation. The stability and convergence of this method are demonstrated both numerically and graphically. Python code is provided to obtain numerical and graphical solutions for the fractional-order subdiffusion bioheat equation.