This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.

This work introduces a novel approach to modeling the photothermal behavior of semiconducting materials by developing a Moore-Gibson-Thompson (MGT) fractional photothermal model that incorporates a generalized Caputo fractional derivative with a tempering parameter. This advanced model is specifically designed to analyze elastic plasmonic wave systems in photothermal environments, offering deeper insights into the interactions between thermal, mechanical, and electromagnetic fields in semiconductors. By including the two-parameter tempered-Caputo fractional derivative, the model accounts for memory effects inherent in the thermal and mechanical behavior of materials exposed to high-energy processes. The model is applied to an infinite semiconducting medium with a drag-free spherical cavity subjected to a dynamically changing thermal field. This setup is highly relevant to semiconductor technology applications, where precise control over thermal and mechanical responses is crucial. The findings of this study could have significant implications for the design and analysis of semiconductor devices, particularly those operating under extreme thermal or electromagnetic conditions.