The Impacts of Atangana–Baleanu Fractional Derivative in Biological Tissues during Thermotherapy

Document Type : Research Paper

Authors
Areej Almuneef 1
Ibrahim Abbas 2
Alaa A. El-Bary 3
Zuhur Alqahtani 1
1 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2 Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt
3 Institute of Basic and Applied Science, Arab Academy for Science, Technology and Maritime Transport, Egypt
10.22055/jacm.2025.48171.5030
Abstract
This study investigates thermal damage in living tissue during thermotherapy by employing the bioheat equation under fractional derivatives. The Atangana-Baleanu (AB) derivative is taken into consideration in the fractional-order formulation using non-singular and local kernels. Analytical solutions are derived in the Laplace domain, facilitating precise examination of the impacts of fractional derivatives and moving heating source speed on skin tissue temperature and thermal injury. The fractional bioheat model reduces to hyperbolic and Pennes models as the relaxation time approaches zero and the fractional order parameter equals one, according to the results. Thermal damages are quantified using the denatured protein range based on Arrhenius' formulation. Numerical findings on temperature distribution and tissue damage are presented graphically. Finally, a parametric analysis highlights critical design variables for optimizing heating efficiency in hyperthermia treatment.
Keywords
Fractional derivatives
Living tissues
Thermal damages
Laplace transform
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 1
Winter 2026
Pages 51-59