Stability and entropy production in fractional bio-heat transport models via generalized (q, τ)-entropy

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-Numerical simulations demonstrate the evolution of temperature profiles and entropy dynamics, revealing the interplay between fractional memory, metabolic heat generation, and entropy-induced resistance. A stability theorem this framework offers a physically consistent and flexible approach grounded in non-equilibrium statistical mechanics and bio-thermal regulation, making it suitable for applications in complex biological media with long-range.