Biothermomechanical interactions in two-dimensional living tissue under Atangana–Baleanu fractional derivatives

Abstract

This study investigates the impact of the Atangana-Baleanu (AB) fractional derivative in two-dimensional living tissue under pulse heat flux. Atangana-Baleanu (AB) derivatives with local and non-singular kernels are accounted for in the fractional-order formulation. Unlike classical models such as Pennes' equation, which assumes infinite thermal propagation speed, the proposed framework captures finite thermal and mechanical wavefronts. The half-space surface's border experiences a pulse-shaped heat flux, yet the edge is fixed in displacement and free of shear stress. The analytical solutions for the variables are derived using Laplace and Fourier transforms combined with the eigenvalue approach methodology. The numerical calculations have been done, and the finding are graphically displayed to estimate the impacts of fractional order parameter and heat flux pulse time in temperature distribution and mechanical responses. Numerical results indicate that thermal and mechanical waves propagate through living tissues over a finite distance, effectively addressing the unrealistic predictions of Pennes' model.