On the well posedness and the stability of a thermoelastic Gurtin–Pipkin–Timoshenko system without the second spectrum

In this work, we establish the well-posedness and the asymptotic stability of a linear thermoelastic Gurtin–Pipkin–Timoshenko system free of second spectrum. We give a detailed proof of the well-posedness, using the semigroup theory and with the help of some new operators. Then, we prove that the system is exponentially stable irrespective of the parameters. Our result generalizes an earlier result, one in the paper of Keddi, Messaoudi, and Alahyane [Journal of Thermal Stresses 46 (2023), 823–838].