Application of fractional derivatives in the Guyer and Krumhansl heat transfer control model for magneto-thermoelastic analysis of transversely isotropic annular cylinders

In this study, we presented a novel fractional nonlocal thermoelastic heat conduction model that extends the Guyer–Krumhansl framework by incorporating size-dependent nonlocal thermal effects and non-Fourier heat conduction characteristics. The model extends the traditional approach using the single-phase-lag (SPL) method derived from Moore–Gibson–Thompson (MGT) heat theory. By employing the Atangana–Baleanu (AB) fractional derivative with a non-singular kernel, we integrated nonlocal features through fractional derivatives, enhancing its applicability to complex thermal behaviors in materials exhibiting combined nonlocal and fractional dynamics. To validate the model, thermoelastic interactions were examined in a long, hollow cylinder subjected to a uniform electromagnetic field. The outer surface was thermally insulated and traction-free, while the inner surface, also traction-free, experienced thermal shock. Governing equations were solved using the Laplace transform method, and numerical solutions were obtained via the Dubner–Abate algorithm. The results were compared with conventional and generalized thermoelastic models to assess accuracy and effectiveness. Additional analysis explored material properties through graphical data, considering various fractional orders and operators, thereby enriching the understanding of system behavior under different conditions. The findings demonstrated the advantages of the fractional nonlocal thermoelastic model in capturing complex thermal interactions within advanced materials, contributing significantly to heat conduction theory.