A Two‑Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

This article presents a new thermoelastic model that incorporates fractional‑order deriva‑
tives 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 re‑
sponses of a solid cylinder with a restricted surface and exposed to a moving heat flux were exam‑
ined 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.