Abstract The present study examines the impact of a three-phase lags thermoelastic infinite medium with a spherical cavity subjected to thermal shock in the temperature of its internal boundary. In this study, a new time-fractional three-phase-lag thermoelasticity model with memory-dependent derivatives is utilized. From the suggested model, we recover certain previous thermoelasticity models as special instances. Laplace transform techniques are used. The solution to the problem in the transformed domain is obtained by using the Gaver-Stehfest algorithm. The validity of the proposed theory is evaluated through a comparison with the existing literature. The numerical computations are conducted and represented graphically. The numerical values of field variables show significant differences for a specific material, highlighting important points related to the prediction of the new model. The article’s physical viewpoints could be helpful in the development of novel materials. Keywords: Thermoelastic; three-phase-lags; memory-dependent derivative; fractional calculus; spherical cavity; non-simple. Three‑phase‑lags thermoelastic infinite medium model with a spherical cavity via memory‑dependent derivatives Nin Chandel 1* , Lalsingh Khalsa 1 , Sunil Prayagi 2 , Vinod Varghese 1 RESEARCH ARTICLE © The Scientific Temper. 2024 Received: 08/01/2024 Accepted: 10/02/2024 Published : 15/03/2024 1 Department of Mathematics, M.G. College, Armori, Gadchiroli, India. 2 Department of Mechanical Engineering, Yeshwantrao Chavan College of Engineering Nagpur *Corresponding Author: Nitin Chandel, Department of Mathematics, M.G. College, Armori, Gadchiroli, India, E-Mail: nitinsinghchandel9@gmail.com How to cite this article: Chandel, N., Khalsa, L., Prayagi, S., Varghese, V. (2024). Three-phase-lags thermoelastic infinite medium model with a spherical cavity via memory-dependent derivatives. The Scientific Temper, 15(1):1726-1732. Doi: 10.58414/SCIENTIFICTEMPER.2024.15.1.21 Source of support: Nil Conflict of interest: None. Introducon The classical uncoupled thermoelasticity model has two issues that do not align with observed physical phenomena: the equilibrium state of heat conduction does not impose constraints on elastic terms, and the heat conduction equation produces an unlimited speed of propagation for thermal waves. Biot (1956) formulated the theory of coupled thermoelasticity (CTE), which integrates governing equations and resolves the initial dilemma of the classical theory. However, the second paradox, with the coupled theory’s heat conduction equation being a parabolic type, was still as is. Lord and Shulman (1967) formulated a novel The Scientific Temper (2024) Vol. 15 (1): 1726-1732 E-ISSN: 2231-6396, ISSN: 0976-8653 Doi: 10.58414/SCIENTIFICTEMPER.2024.15.1.21 https://scientifictemper.com/ law of heat conduction, which is classified as hyperbolic and predicts finite propagation speeds for both thermal and mechanical waves. Miller (1971) proposed a limit on a class of constitutive equations, imposing an entropy inequality. Green and Laws (1972), Green and Lindsay (1972), and Suhubi (1975) expanded upon this imbalance. Youssef (2005); Youssef (2005) successfully addressed challenges about generalized thermo-elasticity for an in- finite material with a spherical cavity. Tzou (2014) introduced a dual-phase-lag (DPL) model to study microstructural interactions within solid heat conductors at a microscopic scale, incorporating delay time translation of heat flux vector and temperature gradient. Youssef (2016) successfully solved the initial mathematical model of thermoelasticity with fractional order strain for a homogeneous isotropic one-dimensional thermoelastic half-space, utilizing various thermo-elasticity models. The present study presents a theoretical framework based on a two-temperature, three-phase lag (TPL) thermoelastic model to elucidate the influence of heat propagation within an infinite medium featuring a spherical cavity. To tackle the challenge of infinite speed propagation, the Fourier model has been modified through the incorporation of a specific time constant, referred to as the phase lag of the heat flux, temperature gradient, and displacement gradient. The closed-form solutions of temperature distribution components across the proposed model are derived using the integral transform approach. The Gaver- Stehfest procedure is employed to derive the numerical Laplace inversion.