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Stabilization for Some Fractional-Evolution Systems

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This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the abstract results of chapter 1 on concrete examples, and the third of which studies the stabilization of fractional evolution systems with memory.

Author(s): Kaïs Ammari, Fathi Hassine, Luc Robbiano
Series: SpringerBriefs in Mathematics
Publisher: Springer
Year: 2022

Language: English
Pages: 72
City: Cham

Contents
1 Introduction
2 Fractional Feedback Stabilization for a Class of Evolution Systems
2.1 Introduction
2.2 Augmented Model
2.3 Well-Posedness
2.4 Strong Stabilization
2.5 Lack of Uniform Stabilization
2.6 Non-Uniform Stabilization
3 Applications to the Fractional-Damped Wave Equation
3.1 Internal Fractional-Damped Wave Equation
3.2 Fractional-Kelvin-Voigt Damped Wave Equation
3.3 Pointwise Fractional-Damped String Equation
4 Stabilization of Fractional Evolution Systems with Memory
4.1 Introduction
4.2 Well-Posedness and Exponential Stabilization
4.3 Polynomial Stabilization
4.4 Extension to Some Integro-Differential Equation
Bibliography