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

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.