Fractional DPL Thermoelasticity With Rabotnov Kernel in a Rotating Stressed Medium With Spherical Cavity

ABSTRACT This study introduces a novel fractional dual‐phase‐lag (DPL) thermoelastic model that incorporates the nonsingular Rabotnov exponential kernel to analyze wave propagation in a rotating, unbounded medium with a spherical cavity under initial hydrostatic stress and a constant magnetic field. Unlike traditional fractional models with singular kernels, the proposed approach uniquely captures memory‐dependent and nonlocal interactions, providing superior accuracy in modeling anomalous heat conduction and stress relaxation in high‐speed rotating systems. By integrating fractional derivatives with phase delays, the model effectively accounts for thermal and mechanical wave dispersion, offering new insights into materials with history‐dependent behaviors. Using Laplace transforms and numerical inversion, temporal solutions are derived for temperature, displacement, stresses, and induced electromagnetic fields. The results emphasize the significant influence of the Rabotnov kernel's parameters and the fractional order on material responses. This work advances the field of thermoelasticity by presenting a versatile and physically realistic framework with broad implications for engineering applications, such as aerospace structures and geophysical systems.