Fractional-Order Photo-Thermoelastic Wave Propagation in Double-Porosity Semiconductor Media with Memory-Dependent and Decaying Heat Source

Kh. Lotfy^1,2*Saurav Sharma²Imed Bachar²Ibrahim S Elshazly²Eslam Elidy²Ramdan S Tantawi²

• ¹Faculty of Science, Zagazig University, Zagazig, Egypt
• ²Zagazig University, Zagazig, Al Sharqia, Egypt

This study develops a comprehensive theoretical framework for the propagation of photo-thermoelastic waves in a two-dimensional (2D), double-porosity semiconductor medium governed by a fractional-order generalized thermoelasticity theory. The classical Lord–Shulman (LS) model is extended through the incorporation of a Caputo-type fractional time derivative in the heat conduction equation, capturing memory-dependent and nonlocal thermal effects absent in traditional models. The coupled system of equations accounts for mechanical deformation, temperature variations, and photoexcitation-induced carrier dynamics under a linearized regime. The analysis is conducted in a 2D elastic half-space, with spatial and temporal field variables governed by harmonic wave assumptions. The resulting fractional differential system is solved using the normal mode method, yielding analytical expressions for the main physical fields. Numerical simulations using silicon material parameters are presented to explore the effects of fractional order, decay parameters on wave propagation characteristics. Results reveal that the fractional-order model significantly alters wave speed and stress distribution, underscoring the critical role of memory effects and double-porosity architecture in next-generation semiconductor applications.