Stability and regularity of fractional coupled system of MGT‐thermoelasticity of type III

Abstract In this paper, we consider the stability and regularity of a coupled system of Moore–Gibson–Thompson equation and Type III heat conduction equation in which the orders of the fractional power of operator are , . By employing the semigroup method, we establish the well‐posedness of the system. The stability of the system is analyzed using the frequency domain method and the multiplier technique, leading to the conclusion that the system is exponentially stable for . The regularity of the system is also established. Precisely, the semigroup associated with the system is analytic when , whereas it lacks analyticity when . The semigroup associated with the system belongs to the Gevrey class for and , and to the Gevrey class for and . The semigroup lacks the Gevrey class when .