Non-Integer Order Calculus and its Applications

1. Front Matter

   Pages i-x

   PDF

2. Mathematical Foundations

   1. Front Matter

      Pages 1-1

      PDF

   2. Decentralized Stabilization of Fractional Positive Descriptor Discrete-Time Linear Systems

      • Tadeusz Kaczorek

      Pages 3-13

   3. Non-invasive Control of the Fractional Hegselmann–Krause Type Model

      • Ricardo Almeida, Agnieszka B. Malinowska, Tatiana Odzijewicz

      Pages 14-27

   4. Differintegarator Based on Fractional Calculus of Convex Functions

      • Radosław Cioć

      Pages 28-35

   5. The AQM Dropping Packet Probability Function Based on Non-integer Order \(PI^{\alpha }D^\beta \) Controller

      • Adam Domański, Joanna Domańska, Tadeusz Czachórski, Jerzy Klamka, Jakub Szyguła

      Pages 36-48

   6. New Numerical Techniques for Solving Fractional Partial Differential Equations in Conformable Sense

      • Mehmet Yavuz, Necati Özdemir

      Pages 49-62

   7. Implementation of Low-Pass Fractional Filtering for the Purpose of Analysis of Electroencephalographic Signals

      • Aleksandra Kawala-Janik, Waldemar Bauer, Amir Al-Bakri, Chase Haddix, Rajamanickam Yuvaraj, Katarzyna Cichon et al.

      Pages 63-73

   8. Grünwald-Letnikov-Laguerre Modeling of Discrete-Time Noncommensurate Fractional-Order State Space LTI MIMO Systems

      • Krzysztof J. Latawiec, Rafał Stanisławski, Marian Łukaniszyn, Marek Rydel, Bogusław R. Szkuta

      Pages 74-83

   9. Stability Analysis of Fractional Discrete-Time Linear Scalar Systems with Pure Delay

      • Andrzej Ruszewski

      Pages 84-91

   10. Duality Properties of Variable-Type and -Order Differences

       • Wiktor Malesza, Dominik Sierociuk

       Pages 92-101

   11. A PLC Implementation of PSE Approximant for Fractional Order Operator

       • Krzysztof Oprzedkiewicz, Edyta Gawin, Wojciech Mitkowski

       Pages 102-112

   12. Memory-Effective Modifications of PSE Approximation

       • Krzysztof Oprzedkiewicz

       Pages 113-125

   13. Comparison Fixed-Point and Floating-Point Implementation of Noninteger Filter of STM Microcontroller

       • Waldemar Bauer, Wojciech Słowik

       Pages 126-134

   14. Fractional Derivative Approach in Modeling of a Nonlinear Coil for Ferroresonance Analyses

       • Łukasz Majka

       Pages 135-147

3. Modeling

   1. Front Matter

      Pages 149-149

      PDF

   2. An Extended Kalman Filter for Time Delays Inspired by a Fractional Order Model

      • Benedikt Haus, Paolo Mercorelli

      Pages 151-163

   3. Fractional Linear Systems with Memory Deficiency and Their State-Space Integer-Order Approximation

      • Stefan Domek

      Pages 164-179

4. Fractional Order System Analysis

   1. Front Matter

      Pages 181-181

      PDF

   2. Analysis of Fractional Electrical Circuit Using Caputo and Conformable Derivative Definitions

      • Ewa Piotrowska, Krzysztof Rogowski

      Pages 183-194

This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).
As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.
Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. 
The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:
•         Mathematical foundations
•         Fractional systems analysis and synthesis•         System modeling
Seven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.

• Electrical Engineering
• Non-Integer Systems
• Fractional Systems
• Non-Integer Order Calculus
• Non-Integer Order Systems
• Fractional Difference
• Fractional Deńvative
• Caputo Derivative
• Grunwald-Letnikov Derivative
• Riemann-Liouville Derivative
• Fractional Calculus
• Discrete Fractional Calculus
• Fractional Order Transfer Function
• Fractional Order Regulators
• Characteristic Exponents
• Fractional Positive Systems
• Controllability
• Controllability
• Stability
• complexity

• Institute of Applied Computer Science, Lodz University of Technology, Lodz, Poland

  Piotr Ostalczyk, Dominik Sankowski, Jacek Nowakowski

Policies and ethics