Fractional-order strain of an infinite annular cylinder based on Caputo and Caputo–Fabrizio fractional derivatives under hyperbolic two-temperature generalized thermoelasticity theory

Abstract A new mathematical model of a thermoelastic annular cylinder that is infinite, isotropic, and homogeneous has been constructed in this paper. The model is developed within the framework of the theory of hyperbolic two-temperature generalized thermoelasticity, considering fractional-order strain applying Caputo and Caputo–Fabrizio derivatives with fractional order. The inside pounding surface of the cylinder is subjected to a thermal shock, while the outer pounding surface remains unaffected in terms of temperature increment and volumetric strain. Once the governing equations were derived, The Laplace transforms were utilized, and their inversions were obtained numerically by using the Tzou iteration method. The numerical results of solutions have been represented in different figures. Various values of fractional-order parameters and two-temperature parameters have been used to illustrate their effect on the mechanical and thermal waves. Stress, strain, and displacement distributions are all profoundly affected by the fractional-order parameter; however, the conductive and dynamic temperatures are unaffected. The results of this work lead to the fact that the mechanical and thermal waves propagate at finite speeds when the hyperbolic two-temperature model is applied.