Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21) / edited by Andrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk.

Format:

Book

Contributor:

Ostalczyk, Piotr, editor.

Dzieliński, Andrzej, editor.

Sierociuk, Dominik, editor.

Series:

Lecture Notes in Networks and Systems, 2367-3389 ; 452

Language:

English

Subjects (All):

Automatic control.

Robotics.

Automation.

Dynamics.

Nonlinear theories.

System theory.

Mathematical analysis.

Control, Robotics, Automation.

Applied Dynamical Systems.

Complex Systems.

Integral Transforms and Operational Calculus.

Local Subjects:

Control, Robotics, Automation.

Applied Dynamical Systems.

Complex Systems.

Integral Transforms and Operational Calculus.

Physical Description:

1 online resource (268 pages) : illustrations (chiefly color).

Edition:

1st ed. 2022.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2022.

Language Note:

English

Summary:

This book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications. The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6–8 September 2021. The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6–8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one. In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character.

Contents:

Intro

Preface

Contents

Some Proposals for a Renewal in the Field of Fractional Behaviour Analysis and Modelling

1 Introduction

2 Fractional Order Models and Associated Drawbacks

3 Some New Kernels

3.1 Kernels 1 ( t )

3.2 Kernel 2 ( t )

3.3 Kernel 3 ( t )

3.4 Kernel 4 ( t )

4 Volterra Equations

5 Other Alternative Models to Capture Power Law Type Behaviours

5.1 Distributed Time Delay Systems

5.2 Nonlinear Models

5.3 Partial Differential Equations (Diffusion Equations) with Spatially Variable Coefficients

6 Conclusion

References

Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used

2 Problem Analysis with Caputo's Definition

3 Analysis with Other Definitions

3.1 The Riemann-Liouville Definition

3.2 The Grünwald-Letnikov Definition

4 Need to Take into Account All of the Model Past

5 Conclusion

The Complex Order Fractional Derivatives and Systems are Non Hermitian

2 The Hermitian Property of Real Order Fractional Derivatives

3 Complex Order Derivatives

3.1 Non Hermitian Character

3.2 Using the Hilbert Transform

4 The Hermitian Part

Transient Regime of Fractional RLC Circuit

2 Model Formulation and Analytical Solution

3 Conclusion

Modelling Cardiovascular Diseases with Fractional-Order Derivatives

2 Description of the Cardiovascular System

3 Fractional-Order Model of the Cardiovascular System

4 Modelling of Pathologies

5 Conclusions

Frequency Domain Modeling of an IPMC-Based Artificial Eukaryotic Flagellum Swimming Robot

2 Modeling of IPMC Actuators

3 Experiments

3.1 Swimming Robot

3.2 Set-up.

3.3 Measured Frequency Responses

4 Identified Dynamic Models for Control

Accuracy Analysis of Approximated Fractional Order Transfer Function with Pole and Zero

2 Preliminaries-The Charef Approximation

3 The Considered Transfer Function with Zero and Pole

4 The Proposed Approximation of the Transfer Function

5 Examples

5.1 Example 1

5.2 Example 2

5.3 Example 3

6 Final Conclusions

Fractional Order Models Are Doubly Infinite Dimensional Models and Thus of Infinite Memory: Consequences on Initialization and Some Solutions

2 A Physical and Systemic Analysis of Fractional Models

2.1 Models Definition

2.2 Poles and Time Constants Distribution and Infinite Memory

2.3 Spatial Definition and Infinite Memory

3 Other Modelling Solutions

3.1 Kernels with Limited Memory

3.2 Volterra Integro-Differential Equations

3.3 Time Delay Models

3.4 Nonlinear Models

3.5 Time Varying Models

3.6 Diffusion Equation with Spatially Variable Coefficients

4 Conclusion

Stability Analysis of COVID-19 via a Fractional Order Mathematical Model

1 Introduction and Preliminaries

2 Description of the SEIR Covid-19 Model

3 Stability Analysis of the Model

3.1 Local Stability Analysis

4 Numerical Simulation and Discussion

5 Concluding Remarks

Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

2 Evidence of the Fractionnal Asymptotic Behavior for Some Fractal Surfaces

3 Power-Law Non Linear Dynamical Modeling

Vectorization Calculation Method of the Fractional-Order Mem-Elements

2 Vectorization of Fractional-Order Memristor, Meminductor and Memcapacitor.

2.1 HP Model and Fractional Order Mem-Elements

2.2 The Vectorization of Fractional Order Mem-Elements

2.3 Different Kinds of Mem-Elements Superposition

Which Kind of Fractional Partial Differential Equations Has Solution with Exponential Asymptotics?

2 Exponential Asymptotics

Detection of a Fractal Element with Complex-Conjugated Power-Law Exponents in Living Systems: Analysis of the Temporal Evolution of Impedance Measurements in the Unblown Bud Plumeria Flower (Frangipani Plumeria)

1 The Theory of the Branching System in the Frequency Domain

2 The Basic Plots Demonstrating the Fit of the Found Functions Eq. (7, 8) to the Measured Data

3 The Results Obtained

4 Mathematical Appendix

4.1 How to Obtain the Functional Eq. (4)?

4.2 How to Obtain the Solution (6) of the Functional Eq. (4)?

Prabhakar Discrete-Time Generalization of the Time-Fractional Poisson Process and Related Random Walks

2 The Prabahakar Discrete-Time Counting Process

3 Prabhakar Discrete Time Random Walk Model

4 Conclusions

A Temporal Second-Order Scheme for Time Fractional Mixed Diffusion and Wave Equation with an Initial Singularity

1 Model Problem

2 Crank-Nicolson Formulae and Error Analyses

2.1 C-N Formulae to Approximate Fractional Operators

2.2 Error Analyses

3 A Numerical Scheme on Graded Meshes

4 Numerical Examples

Optimized Current and Speed Fractional-Order PID Control in Electrical Drives

2 Mathematical Preliminaries

3 Controllers Optimization

4 Solving the Optimization Problem

5 Simulation Results

Operational Calculus with Applications to Generalized Two-Sided Fractional Derivative.

1 Introduction

2 Generalized Two-Sided Fractional Derivative

3 Operational Calculus

4 Illustrative Examples

A Remark on the Memory Property of Fractional Difference Operators

2 Main Results

Mikusiński's Operational Calculus Applied in General Classes of Fractional Calculus

2 The Riemann-Liouville and Caputo Settings

2.1 Informal Description

2.2 Formal Analysis

3 The General Setting of Fractional Calculus with Respect to Functions

4 Other Generalisations and Extensions

Control of All Axis in 3D Crane Using FOPID Controllers Optimized with GWO Algorithm

2 FOPID Controller

3 Grey Wolf Optimizer

4 Mathematical Model of the 3D Crane

5 Implementation of Simulation

6 Results of Simulation

7 Conclusion

Axial Stabilizing CRONE Controller of an Active Magnetic Bearing with Strong Performance and Control-Effort Specifications

2 Description of the Axial Rotor Dynamic and the AMB Control Loop

2.1 System Short Description

2.2 AMB Modelling

2.3 Dynamic of the Axial Deviation Measurement

2.4 Simulator Test Bench

3 Design of the Control-System

3.1 Linear Model Description

3.2 CRONE Design of a Robust Feedback Digital Controller

3.3 Optimal Loop Shaping of the CRONE Open Loop Nominal Transfer Function

3.4 Rational Approximation of the Fractional Order Controller

4 Simulation Assessments

Matsuda Method Adapted to Identify Fractional Order Transfer Functions

2 The Original Matsuda Method

2.1 Continued Fractions

2.2 Identification

3 Identifying Implicit Fractional Order Transfer Functions.

4 Identifying Explicit Commensurable Fractional Order Transfer Functions

5 Examples of Application

5.1 Metaheuristics

5.2 Identifying Filters with One Pole

5.3 Identifying Filters with Two Poles

5.4 General Fractional Order Filter Design

6 Discussion and Conclusions

An Existence Result for a Fractional Integral Boundary Value Problem of Mixed Type with Impulses

1 The Impulsive Problem

1.1 Preliminaries

2 Main Result

3 Example

Pattern Formation in Activator-Inhibitor Fractional Reaction-Diffusion Systems

1 Generalized Basic Two-Component Activator-Inhibitor System

2 Linear Stability Analysis

2.1 Standard Reaction-Diffusion System

2.2 Space-Fractional Reaction-Diffusion System

2.3 Time-Fractional Reaction-Diffusion System

3 Pattern Formation in Fractional RDS

3.1 Basic Activator-Inhibitor Mathematical Models

3.2 Complex Spatio-Temporal Dynamics in Fractional RDS

Stability Results for Two-Term Fractional-Order Difference Equations

2 Preliminaries

3 Stability Results for Two-Term Fractional-Order Difference Equations

4 Fractional-Order Dependent Stability Results

Global Thermal Modeling of Lung Heat Transfer with Blood Perfusion

2 Two-Port Network Models

2.1 Classic Two-Port Network

2.2 Bio-heat Two-Port Network

2.3 T Circuit

3 Lung Global Model

4 Simulations and Results

Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations

2 Finite Difference Scheme

3 Numerical Results

CRONE Controller Synthesis Improvement by an Additional Feedback

2 Mathematical Preliminaries.

2.1 Fractional Integral and Fractional Derivative.

Notes:

Includes author index

Other Format:

Print version: Dzielinski, Andrzej Proceedings of the International Conference on Fractional Differentiation and Its Applications (ICFDA'21)

ISBN:

3-031-04383-9