Abstract
In the presented work, a modified fractional Kelvin–Voigt model (KVM) is introduced to explain the time-dependent behavior of viscoelastic materials based on thermo-viscoelasticity theory and fractional calculus. The fractional KVM involves mechanical viscoelastic parameters and differential operators of fractional orders. In addition, the governing system equations are constructed within the framework of generalized thermoelasticity with three different delay times (TPL). The resulting derived model is used to study the thermo-viscoelastic interactions in a rotating transversely hollow cylinder under the influence of thermal loads and due to a magnetic field of constant intensity. The system of equations is solved, and solutions for non-dimensional physical quantities such as temperature, radial displacement, and thermal stresses are derived by applying the Laplace transform technique. To assess the influences of fractional order, relaxation factors and delay time parameters using different models of thermo-viscoelasticity in the presence and absence of fractional orders, several comparisons are made in tables and figures. Finally, according to the discussion of the numerical results, the prominent role of these parameters in the propagation behavior of mechanical and thermal waves is revealed.