Stochastic thermoelastic wave dynamics in triple-porous biological tissue: a fractional-order nonlocal framework

Purpose This study aims to develop a stochastic bio-thermoelastic framework to investigate heat transport and thermoelastic wave propagation in multi-porous human skin under thermal loading, incorporating thermal memory, nonlocal interactions, hierarchical porosity and stochastic fluctuations. Design/methodology/approach A fractional-order Lord–Shulman thermoelastic model is coupled with Klein–Gordon-type nonlocal elasticity and a triple-porosity representation of macro-, micro- and nano-scale pore networks. Stochastic thermal excitation is introduced through a Wiener process. The governing equations are non-dimensionalized and solved using normal mode analysis to obtain analytical expressions for displacement, temperature, porosity and stress. The stochastic responses are characterized in terms of their expectation, variance and autocorrelation. Findings The results show that stochastic thermal fluctuations significantly influence the thermal and mechanical responses and alter thermoelastic wave propagation. The fractional-order parameter controls memory-dependent heat transport, while nonlocal interactions modify temperature, stress and porosity fields. The coupling among the three pore networks further affects the overall thermo-mechanical response. Research limitations/implications The model considers a linearized thermoelastic response and Wiener process-based thermal fluctuations. Extensions incorporating nonlinear and anisotropic tissue behavior, vascular perfusion, biochemical effects and patient-specific geometries would broaden its applicability. Practical implications The proposed framework can assist in predicting thermo-mechanical tissue responses and assessing thermal effects in applications such as hyperthermia, laser surgery and thermal ablation, with potential relevance to treatment planning and biomedical device design. Originality/value This study provides a unified analytical framework integrating fractional memory, Klein–Gordon nonlocality, triple porosity and stochastic thermal excitation for human skin. It offers new insights into the combined effects of memory, nonlocality, hierarchical porosity and randomness on bio-thermoelastic wave propagation.