Generalized thermoelastic interactions in porous asphaltic material under fractional time derivative

This study investigates generalized thermoelastic interaction in porous asphaltic materials subjected to thermal loading, using fractional model with time-delay effects. The framework incorporates the Riemann-Liouville fractional derivative to account for memory-dependent heat conduction, extending classical thermoelasticity into a more accurate and comprehensive domain. The Lord–Shulman model with one relaxation time is adopted to describe the coupling between mechanical and thermal responses. The governing equations are solved using Laplace transform and the eigenvalues approach, and the Stehfest algorithm is employed for numerical inversion. A detailed analysis is presented for temperature distribution, displacement, and stress fields in both solid and liquid phases of the porous medium under traction-free and thermally loaded boundary conditions. The numerical calculations show how the different sets of fractional parameters have impacted the temperature, stress, and displacement in the solid and liquid phases. Eventually, the visual representation of the data illustrates the distinctions between the fractional poro-thermoelasticity and classical coupled thermoelasticity formulations.