To extend the applicability and accuracy of the generalized thermoelasticity theory of thermoelasticity theory for one-dimensional problems involving a moving heat source, this study proposes a fractional-order thermoelasticity coupling theoretical model based on the Green-Lindsay theory and the Caputo-Fabrizio fractional-order derivative. The model's uniqueness and reciprocity are well established. To show its application, we analyzed the thermoelastic coupled dynamic response of a fixed-end rod subjected to a moving heat source. Using Laplace transforms and its numerical inverse method, the distribution patterns of non-dimensional displacement, temperature, and stress were obtained. A comprehensive analysis was conducted to investigate the effects of the fractional coefficient, two thermal relaxation time factors, and moving heat source speed on non-dimensional displacement, temperature, and stress. The findings reveal that the fractional coefficient and the speed of the moving heat source significantly influence all non-dimensional physical variables. While the two distinct thermal relaxation time factors have a minimal influence on the non-dimensional temperature, they exert a more pronounced effect on non-dimensional displacement and stress.
