Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations

Abstract

In this study, we examine Timoshenko systems with boundary conditions featuring two types of fractional dissipations. By applying semigroup theory, we demonstrate the existence and uniqueness of solutions. Our analysis shows that while the system exhibits strong stability, it does not achieve uniform stability. Consequently, we derive a polynomial decay rate for the system.