Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating

This manuscript introduces a novel mathematical formulation employing fractional-order principles to analyze the response of skin tissue exposed to ramp-type heating within the framework of the refined Lord–Shulman generalized thermoelasticity model. The classical, simple Lord–Shulman, and refined Lord–Shulman models are each examined. The governing equations for these three models are derived, and a general solution for the initial and boundary condition problem is obtained using the Laplace transform approach and its inverse. Numerical results are illustrated through figures, providing a comparative analysis across various theories and fractional-order values to elucidate the impact on temperature, displacement, and dilatation distributions. The numerical and graphical exploration of the influence of ramp-type heat on temperature, displacement, and dilatation distributions is conducted, considering different theoretical frameworks. The reduction in the conductivity caused by the fractional parameter and its ensuing effects on temperature, displacement, and stress are determined.