Fractional-Order Nonlinear Systems
Fractional-Order Nonlinear Systems

Author: Ivo Petráš

Publisher: Springer Science & Business Media

Published: 2011-05-30

Total Pages: 218

ISBN-13: 3642181015

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"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

Introduction to Fractional Differential Equations
Introduction to Fractional Differential Equations

Author: Constantin Milici

Publisher: Springer

Published: 2018-10-28

Total Pages: 199

ISBN-13: 3030008959

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This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus – a major, emerging tool relevant to all areas of scientific inquiry. The authors present examples based on symbolic computation, written in Maple and Mathematica, and address both mathematical and computational areas in the context of mathematical modeling and the generalization of classical integer-order methods. Distinct from most books, the present volume fills the gap between mathematics and computer fields, and the transition from integer- to fractional-order methods.

Nonlinear Systems of Fractional Differential Equations
Nonlinear Systems of Fractional Differential Equations

Author: Bashir Ahmad

Publisher: Springer

Published: 2024-08-18

Total Pages: 0

ISBN-13: 9783031625121

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This book studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville, Caputo, ψ-Riemann--Liouville, Hilfer, ψ--Hilfer, Hadamard, Hilfer--Hadamard, Erdelyi--Kober, (k, ψ)-Hilfer, generalized, Proportional, ψ-Proportional, Hilfer--proportional, ψ-Hilfer--proportional type fractional derivative operators, subject to different types of nonlocal boundary conditions. The topic of fractional differential systems is one of the hot and important topics of research as such systems appear in the mathematical modeling of physical and technical phenomena. As the book contains some recent new work on the existence theory for nonlocal boundary value problems of fractional differential systems, it is expected that it will attract the attention of researchers, modelers and graduate students who are interested in doing their research on fractional differential systems.

Nonlinear Differential Equations and Dynamical Systems
Nonlinear Differential Equations and Dynamical Systems

Author: Feliz Manuel Minhós

Publisher: MDPI

Published: 2021-04-15

Total Pages: 158

ISBN-13: 3036507108

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This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

An Introduction to the Fractional Calculus and Fractional Differential Equations
An Introduction to the Fractional Calculus and Fractional Differential Equations

Author: Kenneth S. Miller

Publisher: Wiley-Interscience

Published: 1993-06-02

Total Pages: 384

ISBN-13: 9780471588849

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Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations.

Fractional Order Systems—Control Theory and Applications
Fractional Order Systems—Control Theory and Applications

Author: Omar Naifar

Publisher: Springer Nature

Published: 2021-08-30

Total Pages: 224

ISBN-13: 3030714462

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This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.

Fractional Differential Equations
Fractional Differential Equations

Author: Igor Podlubny

Publisher: Elsevier

Published: 1998-10-27

Total Pages: 366

ISBN-13: 0080531989

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This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

Fractional Dynamics and Control
Fractional Dynamics and Control

Author: Dumitru Baleanu

Publisher: Springer Science & Business Media

Published: 2011-11-19

Total Pages: 302

ISBN-13: 1461404576

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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 Order Systems-Control Theory and Applications
Fractional Order Systems-Control Theory and Applications

Author: Omar Naifar

Publisher:

Published: 2022

Total Pages: 0

ISBN-13: 9783030714475

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This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.