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<p>This work advances the modeling of bioheat transfer in biological tissue by integrating the Atangana–Baleanu fractional derivatives into the bioheat equation, offering a more realistic representation of thermal damage by incorporating memory effects and non-local heat conduction. The fractional derivative (FD) is an effective approach for modeling transient thermal responses in biological tissues. This study introduces FD into the classical Pennes bioheat conduction formulation with one thermal relaxation time, formulating a corresponding bioheat transfer model based on the thermal energy conservation law. The fractional-order formulation employs non-singular and local kernels to account for the Atangana–Baleanu (AB) derivative. The Laplace transforms and numerical inverse transforms approach are employed to analyze thermal responses under pulsed heat flux conditions. The derived models are reduced to the classical Pennes and non-Fourier models, allowing for a comparative analysis of FD in transient bioheat transfer. A numerical investigation explores the impacts of the fractional derivatives, thermal relaxation and heat flux pulse times on temperature variation and distributions.</p>

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A fractional approach to thermal damage modeling in biological tissues under Atangana–Baleanu derivative

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Areej Almuneef,
  • Ibrahim Abbas,
  • Alaa A. El-Bary,
  • Zuhur Alqahtani,
  • Hamid M. Sedighi

摘要

This work advances the modeling of bioheat transfer in biological tissue by integrating the Atangana–Baleanu fractional derivatives into the bioheat equation, offering a more realistic representation of thermal damage by incorporating memory effects and non-local heat conduction. The fractional derivative (FD) is an effective approach for modeling transient thermal responses in biological tissues. This study introduces FD into the classical Pennes bioheat conduction formulation with one thermal relaxation time, formulating a corresponding bioheat transfer model based on the thermal energy conservation law. The fractional-order formulation employs non-singular and local kernels to account for the Atangana–Baleanu (AB) derivative. The Laplace transforms and numerical inverse transforms approach are employed to analyze thermal responses under pulsed heat flux conditions. The derived models are reduced to the classical Pennes and non-Fourier models, allowing for a comparative analysis of FD in transient bioheat transfer. A numerical investigation explores the impacts of the fractional derivatives, thermal relaxation and heat flux pulse times on temperature variation and distributions.