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The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains. [ABSTRACT FROM AUTHOR]

Moore-Gibson-Thompson (MGT) is an equation which appropriately describes the spread of sound waves in gasses and fluids as well as thermal/mechanical waves in elastic bodies. The objective of this article is to theoretically analyze the generalized thermoelasticity models that have been presented as the development of the Fourier's law dealing with the paradox of unlimited propagation velocities of thermal waves. For this purpose, a new model is presented which combines the third type of Green and Naghdi model (GN-III) with the generalized theory including the relaxation time based on the MGT equation. The proposed model may be considered as a generalization of previous thermoelastic theories. To examine the introduced approach, the behavior of thermoelastic waves within a homogeneous isotropic sphere in which its surface is exposed to thermal shock with varying heat source is investigated. The variations in different physical fields of a given substance have been computed by means of Laplace transform technique and an efficient numerical technique is implemented in Laplace inversion procedure. The effect of different forms of heat source are also examined and several comparisons for various thermoelasticity approaches are comprehensively conducted. [ABSTRACT FROM AUTHOR]