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.