On the analyticity of the abstract MGT-Fourier system

Abstract We consider the abstract MGT-Fourier system $${\left\{ \begin{array}{ll} u_{ttt}+\alpha u_{tt}+\beta A^\varrho u_t+\gamma u = \eta A \theta \\ _t+\kappa -\eta u_{tt} - \alpha u_t \end{array}\right. }$$ u ttt + ? tt ? A ? t ? = ? ? ? - in subcritical regime $$\beta >\gamma /\alpha$$ > / , where operator is strictly positive selfadjoint. For any fixed $$\varrho \in [1,2]$$ ? [ 1 , 2 ] we show that associated solution semigroup S ( t ) analytic and exponentially stable as well.