Fractional Dynamical Systems Methods Algorithms And Applications

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Fractional Dynamical Systems: Methods, Algorithms and Applications

Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Fractional Dynamical Systems Methods Algorithms and Applications Book PDF

Author : Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Publisher : Unknown
Page : 0 pages
File Size : 52,8 Mb
Release : 2022
Category : Electronic
ISBN : 303089973X

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Fractional Dynamical Systems: Methods, Algorithms and Applications by Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk Pdf

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 relevant and successful practical applications.

Computational Fractional Dynamical Systems

Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Computational Fractional Dynamical Systems Book PDF

Author : Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 52,8 Mb
Release : 2022-11-15
Category : Mathematics
ISBN : 9781119696957

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Computational Fractional Dynamical Systems by Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena Pdf

A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.

Fractional Dynamical Systems: Methods, Algorithms and Applications

Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Fractional Dynamical Systems Methods Algorithms and Applications Book PDF

Author : Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Publisher : Springer Nature
Page : 398 pages
File Size : 51,9 Mb
Release : 2022-01-04
Category : Technology & Engineering
ISBN : 9783030899721

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Fractional Dynamical Systems: Methods, Algorithms and Applications by Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk Pdf

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 relevant and successful practical applications.

Fractional-order Modeling and Control of Dynamic Systems

Aleksei Tepljakov
Fractional order Modeling and Control of Dynamic Systems Book PDF

Author : Aleksei Tepljakov
Publisher : Springer
Page : 184 pages
File Size : 40,6 Mb
Release : 2017-02-08
Category : Technology & Engineering
ISBN : 9783319529509

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Fractional-order Modeling and Control of Dynamic Systems by Aleksei Tepljakov Pdf

This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.

Advances in Synchronization of Coupled Fractional Order Systems

Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho
Advances in Synchronization of Coupled Fractional Order Systems Book PDF

Author : Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho
Publisher : Springer
Page : 185 pages
File Size : 47,9 Mb
Release : 2018-07-23
Category : Science
ISBN : 9783319939469

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Advances in Synchronization of Coupled Fractional Order Systems by Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho Pdf

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems.

Fractional Dynamics and Control

Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo
Fractional Dynamics and Control Book PDF

Author : Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 45,6 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 1461404576

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Fractional Dynamics and Control by Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo Pdf

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

Fractional Dynamics

Vasily E. Tarasov
Fractional Dynamics Book PDF

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 52,9 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642140037

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Fractional Dynamics by Vasily E. Tarasov Pdf

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Fractional-order Systems and Controls

Concepción A. Monje,YangQuan Chen,Blas M. Vinagre,Dingyu Xue,Vicente Feliu-Batlle
Fractional order Systems and Controls Book PDF

Author : Concepción A. Monje,YangQuan Chen,Blas M. Vinagre,Dingyu Xue,Vicente Feliu-Batlle
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 44,5 Mb
Release : 2010-09-28
Category : Technology & Engineering
ISBN : 9781849963350

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Fractional-order Systems and Controls by Concepción A. Monje,YangQuan Chen,Blas M. Vinagre,Dingyu Xue,Vicente Feliu-Batlle Pdf

Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems. Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided. All the control schemes and applications are presented in the monograph with either system simulation results or real experimental results, or both. Fractional-order Systems and Controls provides readers with a basic understanding of FOC concepts and methods, so they can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.

Computational Fractional Dynamical Systems

Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Computational Fractional Dynamical Systems Book PDF

Author : Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 53,6 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9781119696995

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Computational Fractional Dynamical Systems by Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena Pdf

Computational Fractional Dynamical Systems A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.

Fractional Discrete Chaos: Theories, Methods And Applications

Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham
Fractional Discrete Chaos Theories Methods And Applications Book PDF

Author : Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham
Publisher : World Scientific
Page : 218 pages
File Size : 51,8 Mb
Release : 2023-02-13
Category : Science
ISBN : 9789811271229

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Fractional Discrete Chaos: Theories, Methods And Applications by Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham Pdf

In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.The aims of this book are as follows:

Advances in Metaheuristics Algorithms: Methods and Applications

Erik Cuevas,Daniel Zaldívar,Marco Pérez-Cisneros
Advances in Metaheuristics Algorithms Methods and Applications Book PDF

Author : Erik Cuevas,Daniel Zaldívar,Marco Pérez-Cisneros
Publisher : Springer
Page : 218 pages
File Size : 50,7 Mb
Release : 2018-04-10
Category : Technology & Engineering
ISBN : 9783319893099

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Advances in Metaheuristics Algorithms: Methods and Applications by Erik Cuevas,Daniel Zaldívar,Marco Pérez-Cisneros Pdf

This book explores new alternative metaheuristic developments that have proved to be effective in their application to several complex problems. Though most of the new metaheuristic algorithms considered offer promising results, they are nevertheless still in their infancy. To grow and attain their full potential, new metaheuristic methods must be applied in a great variety of problems and contexts, so that they not only perform well in their reported sets of optimization problems, but also in new complex formulations. The only way to accomplish this is to disseminate these methods in various technical areas as optimization tools. In general, once a scientist, engineer or practitioner recognizes a problem as a particular instance of a more generic class, he/she can select one of several metaheuristic algorithms that guarantee an expected optimization performance. Unfortunately, the set of options are concentrated on algorithms whose popularity and high proliferation outstrip those of the new developments. This structure is important, because the authors recognize this methodology as the best way to help researchers, lecturers, engineers and practitioners solve their own optimization problems.

Mathematical Techniques of Fractional Order Systems

Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Mathematical Techniques of Fractional Order Systems Book PDF

Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Elsevier
Page : 700 pages
File Size : 48,8 Mb
Release : 2018-06-11
Category : Technology & Engineering
ISBN : 9780128135938

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Mathematical Techniques of Fractional Order Systems by Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan Pdf

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many applications in the book

Computing Algorithms with Applications in Engineering

V. K. Giri,Nishchal K. Verma,R. K. Patel,V. P. Singh
Computing Algorithms with Applications in Engineering Book PDF

Author : V. K. Giri,Nishchal K. Verma,R. K. Patel,V. P. Singh
Publisher : Springer Nature
Page : 461 pages
File Size : 42,5 Mb
Release : 2020-03-02
Category : Technology & Engineering
ISBN : 9789811523694

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Computing Algorithms with Applications in Engineering by V. K. Giri,Nishchal K. Verma,R. K. Patel,V. P. Singh Pdf

This book collects high-quality research papers presented at the International Conference on Computing Applications in Electrical & Electronics Engineering, held at Rajkiya Engineering College, Sonbhadra, India, on August 30–31, 2019. It provides novel contributions in computational intelligence, together with valuable reference material for future research. The topics covered include: big data analytics, IoT and smart infrastructures, machine learning, artificial intelligence and deep learning, crowd sourcing and social intelligence, natural language processing, business intelligence, high-performance computing, wireless, mobile and green communications, ad-hoc, sensor and mesh networks, SDN and network virtualization, cognitive systems, swarm intelligence, human–computer interaction, network and information security, intelligent control, soft computing, networked control systems, renewable energy sources and technologies, biomedical signal processing, pattern recognition and object tracking, and sensor devices and applications.

Dynamical Systems

José A. Tenreiro Machado
Dynamical Systems Book PDF

Author : José A. Tenreiro Machado
Publisher : MDPI
Page : 552 pages
File Size : 55,7 Mb
Release : 2018-10-09
Category : Dynamics
ISBN : 9783906980478

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Dynamical Systems by José A. Tenreiro Machado Pdf

Printed Edition of the Special Issue Published in Entropy

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications

Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez
Analog Digital Implementation of Fractional Order Chaotic Circuits and Applications Book PDF

Author : Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez
Publisher : Springer Nature
Page : 212 pages
File Size : 44,5 Mb
Release : 2019-11-11
Category : Technology & Engineering
ISBN : 9783030312503

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Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications by Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez Pdf

This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.