On the uniform stability of a thermoelastic Timoshenko system with infinite memory

The present research is aim at investigating a thermoelastic Timoshenko system with an infinite memory term on the shear force while the bending moment is under the influence of a thermoelastic dissipation governed by Fourier's law. We prove that the system's stability holds for a broader class of relaxation functions. Under this class of relaxation functions $h$ at infinity, we establish a relation between the decay rate of the solution and the growth of $h$ at infinity. Moreover, we drop the boundedness assumptions on the history data. We employ Neumann-Dirichlet-Neumann boundary conditions for our result. In comparison to the bulk of results in the literature, which frequently enforce the "equal-wave-speed" constraint, the present result shows that the infinite memory of the beam and the thermal damping are strong enough to guarantee stability without any conditions on the parameters.