Malaysian Journal of Mathematical Sciences, September 2025, Vol. 19, No. 3
Modified Atangana-Baleanu-Caputo Derivative for Nonlinear Thermal Wave Diffusion in Rigid Conductors: Numerical Approach
Sweilam, N. H., Bahaa El Din, N., Ammar, M. K., and Abo El-Dahab, E. M.
Corresponding Email: nsweilam@sci.cu.edu.eg
Received date: 6 March 2025
Accepted date: 25 April 2025
Abstract:
This paper presents a numerical technique based on finite difference method to study numerically the behavior of a rigid thermal conductor's time-nonlinear couple system of heat wave propagation model of fractional order, where the fractional derivative is treated in the sense of Atangana-Baleanu-Caputo.
It has been demonstrated via Fourier analysis that suggested scheme is unconditionally stable. Numerical experiments have been demonstrated to embed and verify the theoretical outcomes provided in this study and guarantee the effectiveness of the numerical method.
Keywords: modified Atangana-Baleanu-Caputo (MABC) fractional derivatives; propagation of time-nonlinear heat waves; stiff thermal conductor; finite difference method; stability analysis; error estimates
