Thermoelastic response of a nanostructured semi‐infinite medium with memory‐dependent higher‐order derivatives under a moving heat source: A Moore–Gibson–Thomson framework

Thermoelasticity integrates thermal and mechanical responses in materials subjected to coupled loads, with classical models constrained by the assumption of infinite thermal wave speeds. Advanced frameworks, such as the Lord–Shulman, Green–Naghdi, and dual‐phase lag models, address this limitation by introducing finite wave speeds and relaxation times. The Moore–Gibson–Thomson (MGT) model further refines heat conduction through third‐order derivatives, ensuring more realistic wave behavior. Memory‐dependent derivatives (MDD) enhance modeling by capturing historical effects, offering superior computational efficiency compared to fractional derivatives in dynamic scenarios, such as thermal shock or material processing. When combined with Eringen's nonlocal continuum theory, MDD accounts for small‐scale interactions that are critical in nanostructures. This study develops an advanced thermoelastic model that integrates MDD with the MGT equation to analyze a semi‐infinite medium under a moving heat source. The governing equations are solved analytically in the Laplace domain using the eigenvalue method, and numerical inversion is performed to obtain time‐domain solutions. Results for a copper medium, presented through figures and tables, demonstrate the model's capability to predict temperature, displacement, and stress distributions. These findings highlight the significance of memory effects and nonlocal interactions for applications in nanotechnology and engineering design.