Purpose <p>This study develops an extended form of the Green–Naghdi type II (GN-II) thermoelasticity theory by integrating memory-dependent and fractional-order derivatives into the heat conduction model. The aim is to enhance the accuracy and adaptability of modeling thermo-magnetomechanical behaviors in complex materials.</p> Design/methodology/approach <p>Fundamental constitutive equations are derived, and a uniqueness theorem is established to ensure model consistency. The model is applied to a one-dimensional thermoelectric spherical shell subjected to random thermal loading and a constant magnetic field. Numerical inversion of the Laplace transform is performed to obtain time-domain solutions, enabling detailed analysis of thermal, mechanical, and electromagnetic responses.</p> Findings <p>Results demonstrate that nonlinear memory kernels significantly influence the evolution of physical field variables. Comparative analysis with classical GN-II predictions shows that the proposed model yields more accurate and stable results, especially under transient and random thermal conditions.&#xa0;</p> Originality/value <p>The proposed fractional thermoelastic model offers a unified and refined extension of GN-II theory. By incorporating memory and time-delay effects, it provides a more comprehensive framework for analyzing the coupled thermo-magnetomechanical responses of advanced materials and engineering systems.</p>