ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Numerical Analysis and Scientific Computation
Volume 11 - 2025 | doi: 10.3389/fams.2025.1643121
Stability and entropy production in fractional bio-heat transport models via generalized (q, τ)-entropy
Provisionally accepted
Shaher Momani1
Rabha W. Ibrahim2,3*- 1Ajman University, Ajman, United Arab Emirates
- 2Institute of Electrical and Electronics Engineers, New York, United States
- 3Alayen Iraqi University, Nasiriyah, Iraq
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We propose a novel framework for modeling thermal transport in biological tissues based on a fractional bio-heat diffusion equation regularized by a generalized (q, τ)-entropy functional. The model incorporates a Caputo-type (q, τ)-fractional derivative to represent memory-dependent heat transport, while a nonlinear entropy term stabilizes thermal dynamics and captures non-extensive statistical effects. We derive a stability theorem based on the monotonic decay of the generalized entropy functional, and provide numerical simulations demonstrating the evolution of temperature profiles and entropy dynamics. Our outcomes reveal the interplay between fractional memory, metabolic heat generation, and entropyinduced resistance in shaping thermal behavior in biological media. The framework offers a physically consistent and flexible approach grounded in non-equilibrium statistical mechanics and bio-thermal regulation.
Keywords: (Q, τ)-Gamma function, entropy-regularized PDEs, Fractional diffusion, Non-extensive thermodynamics, Cramér-Rao inequality, stability analysis, Fisher information
Received: 08 Jun 2025; Accepted: 06 Aug 2025.
Copyright: © 2025 Momani and Ibrahim. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Rabha W. Ibrahim, Institute of Electrical and Electronics Engineers, New York, United States
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