Thomson influence in an electro-magneto-thermoelastic medium via the Moore–Gibson–Thompson model with memory and nonlocality effects

This study presents a comprehensive investigation of the Thomson effect in an electro-magneto-thermoelastic medium governed by the Moore–Gibson–Thompson (MGT) model, enriched with memory-dependent derivatives (MDDs) and Eringen’s nonlocal elasticity. The proposed framework integrates fractional-order heat conduction, electromagnetic field dynamics, and nonlocal mechanical interactions to capture the coupled behavior of advanced materials under thermal and magnetic stimuli. The governing equations incorporate dual-phase-lag (DPL) heat conduction, Maxwell’s equations, and Lorentz force contributions, enabling a robust description of wave propagation and thermal relaxation phenomena. Analytical solutions were obtained using Laplace and Fourier transforms, and the time‑domain fields were recovered through numerical inversion employing the Korrecktur correction and ε‑algorithm acceleration to ensure stability and convergence. The influence of fractional parameters, memory kernels, and nonlocality is systematically analyzed, revealing their impact on temperature distribution, stress evolution, and induced electromagnetic fields. Comparative analysis shows that Green–Naghdi Type III (GN‑III) produces undamped, strongest thermal waves, DPL moderates the response through phase lags, while the proposed MGT framework with memory and nonlocality yields physically consistent, damped responses suitable for microstructured materials. Thus, GN‑III is strongest in amplitude, but MGT is most realistic for engineering applications. The novelty of this work lies in the development of a fractional MGT electro‑magneto‑thermoelastic model that simultaneously incorporates MDDs, Eringen’s nonlocal elasticity, and the Thomson effect. This unified framework bridges classical thermoelasticity with modern fractional and nonlocal theories, offering new predictive capacity for smart materials and semiconductor applications. This work establishes a versatile modeling paradigm for multi-physics applications, bridging classical thermoelasticity with modern fractional and nonlocal theories. The model is particularly suited for microstructured materials, rotating semiconductors, and magnetically active environments.