Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials

This study proposes a comprehensive heat conduction model that incorporates fractional time derivatives
and two-phase lags to describe the behavior of non-simple thermoelastic materials accurately. Generalized
fractional di{erential operators with non-singular kernels are introduced. This type of fractional derivative
includes the Caputo-Fabrizio and the Atangana-Baleanu fractional derivatives. The model also consists of the
two-temperature idea, which considers the e{ect of microstructure through a two-stage delay approach.
Interactions of a thermoelastic nature caused by the rapid heating of an isotropic substance under the
influence of an external body force were studied as a practical application of the new concept. There has been
some discussion about the e{ect of the discrepancy index and fractional di{erential operators. Finally, the
graphical representations obtained from the numerical simulations were used to explain the behavior of the
studied physical fields. The generalized fractional heat transfer model is demonstrated to be capable of
producing a temperature forecast that is in close agreement with experimental data. As a result, the proposed
model may be useful for solving di{iculties in heat transfer, anomalous transport, and other branches of
engineering analysis