Strong Stability of the Thermoelastic Bresse System with Second Sound and Fractional Delay

The thermoelastic Bresse system is a mathematical model that describes the dynamic behavior of elastic beams accounting for both mechanical deformations and thermal effects. Incorporating concepts such as second sound and fractional delay into this system enhances its ability to model complex physical phenomena. The paper studies a Bresse thermoelastic system with fractional delay and second sound. Firstly, we prove the existence and uniqueness of the solution for our system using semi-group theory. Additionally, we derive an exponential decay estimate for the associated semi-group utilizing suitable multiplier techniques.