Symmetric Memory-Dependent Derivative for Advanced Thermoelastic Diffusion Modeling

Classical and fractional thermoelastic diffusion models often fail to capture microscale heat transport and stress evolution in materials with finite memory and nonlocal interactions. To address these limitations, this paper proposes a Symmetric Bi-directional Memory-Dependent Derivative (SBMDD) that incorporates balanced contributions from past and future states within a finite temporal frame, therefore extending traditional memory-dependent formulations. By using normalized symmetric kernels, the operator improves numerical stability and allows for bounded memory representation. For a thermoelastic strip exposed to thermal shock, a nonlocal thermoelastic diffusion model is created using this framework. The Laplace transform and Heaviside operational approach are used to solve the governing equations analytically, and a fixed Talbot contour inversion is used to retrieve time-domain solutions. Numerical results show that the SBMDD model produces smoother temperature, displacement, and stress profiles compared with classical formulations, highlighting its potential for modeling reversible transport and memory-driven thermoelastic processes in microscale and semiconductor systems.