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.

In this paper, we analyze the stabilization of a wave equation subject to a fractional damping term that varies with time. We begin by proving the well-pos

We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.

In this work, we investigate the stabilization problem for coupled biharmonic Schrödinger equations with fractional internal damping. First, we establish that the system is well-posed using the semigroup theory of linear operators. Second, we demonstrate that the system is strongly stable. Finally, we prove a polynomial decay rate using multiplier techniques combined with the frequency domain method, and we show the lack of exponential decay of the energy in a specific case.

This paper investigates the theoretical and numerical stability of the one-dimensional Bresse system with fractional damping terms in a bounded domain. We first establish the well-posedness of the system. Using the frequency domain approach and a theorem by Borichev and Tomilov, we derive the polynomial decay rate of the system. To validate these theoretical results, we propose a numerical scheme and compare its performance with the Fractional Physics-Informed Neural Network (fPINN). The comparative analysis highlights the effectiveness of traditional numerical methods and fPINNs in capturing the decay rate, offering new insights into the advancement of computational techniques for complex physical systems.