Thermoelastic Oscillations of a Solid Medium with Voids via the Influence of Atangana-Baleanu-Caputo Fractional Derivative

This study employs the Atangana–Baleanu–Caputo fractional derivative within the Moore–Gibson–Thompson heat conduction model to analytically investigate the thermoelastic vibrations in solid medium-containing voids. The ABC–MGT formulation incorporates a non-singular Mittag–Leffler memory kernel, facilitating the modeling of tempered hereditary relaxation in voided thermoelastic media, thereby producing more realistic attenuation and phase lag characteristics in transient responses than conventional integer-order models. Specifically, our novelty lies in developing a coupled thermoelastic–void formulation within an ABC–MGT heat conduction framework, deriving the full governing system and boundary-value solution in the Laplace domain, and providing a systematic parametric analysis showing how the ABC order changes attenuation, phase lag, and stress/void interactions. This approach enables a precise analytical resolution of the problem. The analysis indicates that the presence and size of voids substantially impact the system response variables, with smaller apertures yielding reduced magnitudes. Thus, this analytical investigation introduces a novel methodology for addressing the complex challenges associated with advanced functional materials and high-performance engineering structures.