Skip to main content
SpringerLink
Log in

Fractional Dynamical Systems: Methods, Algorithms and Applications

  • Book
  • © 2022

Overview

Editors:
  1. Piotr Kulczycki

    1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Józef Korbicz

    1. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  3. Janusz Kacprzyk

    1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems
  • Develops more effective and efficient tools and techniques for dealing with complex processes and systems
  • Contains analytic contributions, algorithmic implementation of tools and techniques, and successful practical applications

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 402)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Foundations

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Fractional Systems: State-of-the-Art

      • Rafał Stanisławski
      Pages 3-25

    3. Fractional Systems: Theoretical Foundations

      • Piotr Ostalczyk, Ewa Pawluszewicz
      Pages 27-73

  3. Modeling, Behavior and Properties

    1. Front Matter

      Pages 75-75
      Download chapter PDF

    2. Mixed Logical Dynamical Modeling of Discrete-Time Hybrid Fractional Systems

      • Stefan Domek
      Pages 77-105

    3. Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling

      • Andrzej Dzieliński, Dominik Sierociuk, Wiktor Malesza, Michał Macias, Michał Wiraszka, Piotr Sakrajda
      Pages 107-133

    4. Asymptotic Behavior of Discrete Fractional Systems

      • Adam Czornik, Pham The Anh, Artur Babiarz, Stefan Siegmund
      Pages 135-173

    5. Variable-, Fractional-Order Linear System State-Space Description Transformation

      • Piotr Ostalczyk
      Pages 175-197

    6. Balanced Truncation Model Reduction in Approximation of Nabla Difference-Based Discrete-Time Fractional-Order Systems

      • Rafał Stanisławski, Marek Rydel, Krzysztof J. Latawiec
      Pages 199-220

    7. State Feedback Law for Discrete-Time Fractional Order Nonlinear Systems

      • Ewa Pawłuszewicz, Andrzej Koszewnik, Piotr Burzynski
      Pages 221-245

    8. Some Specific Properties of Positive Standard and Fractional Interval Systems

      • Tadeusz Kaczorek, Łukasz Sajewski
      Pages 247-269

  4. Stability and Controllability

    1. Front Matter

      Pages 271-271
      Download chapter PDF

    2. Global Stability of Nonlinear Fractional Dynamical Systems

      • Tadeusz Kaczorek
      Pages 273-306

    3. Controllability of Fractional Linear Systems with Delays in Control

      • Jerzy Klamka
      Pages 307-330

  5. Applications

    1. Front Matter

      Pages 331-331
      Download chapter PDF

    2. Selected Engineering Applications of Fractional-Order Calculus

      • Wojciech Mitkowski, Marek Długosz, Paweł Skruch
      Pages 333-359

    3. Fractional Order State Space Models of the One-Dimensional Heat Transfer Process

      • Krzysztof Oprzȩdkiewicz, Wojciech Mitkowski
      Pages 361-397
Back to top

Keywords

About this book

This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, because—in general—properties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, and—finally—some examples of relevantand successful practical applications.

Editors and Affiliations

  • Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki, Janusz Kacprzyk

  • Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation