ABSTRACT This study introduces a novel fractional thermoelastic model to analyze the behavior of isotropic three‐dimensional solids by combining the Green‐Naghdi framework, the two‐temperature theory, and the Moore‐Gibson‐Thompson (MGT) equation. The approach incorporates nonlocal memory effects through a two‐parameter Mittag‐Leffler fractional derivative, offering a more sophisticated representation of thermal interactions. The model specifically investigates the response of materials under free surface conditions exposed to laser‐induced convection, characterized by a Gaussian distribution in both time and space. Analytical solutions are derived using a combination of Laplace and multi‐Fourier transform techniques, supplemented by numerical simulations to assess the influence of key parameters. The results reveal that the two‐temperature parameter significantly affects the amplitude and phase of thermal and mechanical responses, while the relaxation time and fractional‐order coefficients determine the decay rates and oscillation patterns of system behavior. This fractional thermoelastic perspective provides deeper insights into thermal dynamics, paving the way for advanced engineering applications in thermal insulation design, high‐efficiency heat exchangers, and next‐generation energy storage systems.
Alhassan et al. (Thu,) studied this question.