1. Introduction
Generalized thermoelastic models have been progressed to eliminate the
contradiction in the infinite velocity of heat propagation concealed in
the classical dynamical coupled thermoelasticity theory (CTE) [1].
In these generalized models, the basic equations contain thermal
relaxation times of hyperbolic type [2-5]. Furthermore, Tzou
[6-8] investigated the dual-phase-lag heat conduction theory (DPL)
by including two different phase-delays correlating with the heat flow
and temperature gradient. Chandrasekharaiah [9] introduced a
generalized model improved from the heat conduction model established by
Tzou [7, 8].
In the recent past, fractional calculus has been effectively applied in
many fields to solve problems in electronics, wave propagation,
modeling, biology, chemistry and viscosity. [10-11]. Alternative
definitions and generalization of fractional derivatives introduced by
[12–14]. Furthermore, several models of thermoelasticity have been
investigated with the fractional derivatives by many researchers
[15-20]. Recently, Abouelregal [21-23] created generalized and
novel models of thermoelasticity using fractional calculus.
The present contribution aims to investigate a generalized
two-fractional-parameter heat conduction model of thermoelasticity with
multi-phase-lags. According to this model and in limited case, we can
derive various classical, generalized and fractional thermoelasticity
models. As an application of this model, we study a semi-infinite medium
subjected a body force and exposed to decaying varying heat. Using the
Laplace transform procedure, we obtain an analytical solution for
various physical fields. Numerical calculations are depicted in tables
and graphs to clarify the effect of the two-fractional parameters,
external force and decaying parameter of the varying heat. Finally, the
results obtained are discussed in detail and also confirmed with those
in the previous literature.