Stabilization for Some Fractional-Evolution Systems

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.

Format: Paperback / softback
Length: 69 pages
Publication date: 21 October 2022
Publisher: Springer International Publishing AG

This comprehensive guide offers unified approaches for stabilizing a selection of fractional evolution systems, serving as a valuable addition to the existing literature on fractional calculus. The book is organized into three chapters, the first of which explores the stabilization of certain abstract evolution equations featuring fractional damping. The second chapter validates the theoretical findings presented in Chapter 1 through the application of concrete examples, while the third chapter delves into the stabilization of fractional evolution systems with memory.

Chapter 1: Stabilization of Abstract Evolution Equations with Fractional Damping

In Chapter 1, we delve into the stabilization of abstract evolution equations with fractional damping. These equations arise in various fields, including physics, chemistry, and engineering, and exhibit complex behavior due to the presence of fractional derivatives. We introduce a set of stabilizing techniques, including Lyapunov functions, adaptive control, and neural network-based methods, to address the challenges posed by fractional damping. By applying these techniques, we can achieve stability and control of fractional evolution systems, enabling them to perform tasks with improved accuracy and reliability.

Chapter 2: Validation of Abstract Results on Concrete Examples

Chapter 2 serves as a bridge between the theoretical concepts discussed in Chapter 1 and practical applications. We present concrete examples that illustrate the effectiveness of the proposed stabilizing techniques. These examples cover a wide range of applications, including fractional differential equations, delay differential equations, and stochastic differential equations. By applying the theoretical principles outlined in Chapter 1, we demonstrate the ability to stabilize these complex systems and achieve desired performance objectives.

Chapter 3: Stabilization of Fractional Evolution Systems with Memory

In Chapter 3, we explore the stabilization of fractional evolution systems with memory. These systems are characterized by the presence of both fractional derivatives and memory effects, which introduce additional complexity into the dynamics. We introduce a novel approach based on the concept of fractional-order sliding mode control (FOSMC) to stabilize these systems. By designing appropriate sliding mode functions and applying FOSMC techniques, we can achieve stability and tracking of fractional evolution systems with memory, even in the presence of external disturbances and uncertainties.

In conclusion, this comprehensive guide provides a valuable resource for researchers and practitioners interested in the stabilization of fractional evolution systems. By offering a unified framework for addressing fractional damping, validation of abstract results on concrete examples, and exploration of stabilization techniques with memory, the book contributes to the advancement of the field and enables the development of more efficient and reliable systems for a wide range of applications.

Weight: 136g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031173424
Edition number: 1st ed. 2022