Fractional Calculus In Analysis Dynamics And Optimal Control

Fractional Calculus In Analysis Dynamics And Optimal Control Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Fractional Calculus In Analysis Dynamics And Optimal Control book. This book definitely worth reading, it is an incredibly well-written.

Fractional Calculus in Analysis, Dynamics, and Optimal Control

Jacky Cresson
Fractional Calculus in Analysis Dynamics and Optimal Control Book PDF

Author : Jacky Cresson
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 50,5 Mb
Release : 2014
Category : Fractional calculus
ISBN : 1629486353

Get Book

Fractional Calculus in Analysis, Dynamics, and Optimal Control by Jacky Cresson Pdf

This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analogue of the classical Pontryagin maximum principle is proved for discrete and continuous fractional optimal control problems. The fourth chapter gives a first mathematical model that allows a rigorous connection to be made between the dynamics of chaotic Hamiltonian systems and fractional dynamics, mixing the previous approaches of G Zaslavsky and R Hilfer. Finally, numerical methods to deal with fractional optimal control problems are discussed and implemented. All the chapters are self-contained and complete proofs are given.

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 : 302 pages
File Size : 50,5 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 9781461404576

Get Book

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.

Applications of Fractional Calculus to Modeling in Dynamics and Chaos

J. F. Gómez-Aguilar,Abdon Atangana
Applications of Fractional Calculus to Modeling in Dynamics and Chaos Book PDF

Author : J. F. Gómez-Aguilar,Abdon Atangana
Publisher : CRC Press
Page : 511 pages
File Size : 40,6 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9781000597615

Get Book

Applications of Fractional Calculus to Modeling in Dynamics and Chaos by J. F. Gómez-Aguilar,Abdon Atangana Pdf

Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences

Fractional Order Processes

Seshu Kumar Damarla,Madhusree Kundu
Fractional Order Processes Book PDF

Author : Seshu Kumar Damarla,Madhusree Kundu
Publisher : CRC Press
Page : 211 pages
File Size : 49,9 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9780429996887

Get Book

Fractional Order Processes by Seshu Kumar Damarla,Madhusree Kundu Pdf

The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.

Fractional Dynamics

Vasily E. Tarasov
Fractional Dynamics Book PDF

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 47,8 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642140037

Get Book

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.

Computational Methods In The Fractional Calculus Of Variations

Ricardo Almeida,Shakoor Pooseh,Delfim F M Torres
Computational Methods In The Fractional Calculus Of Variations Book PDF

Author : Ricardo Almeida,Shakoor Pooseh,Delfim F M Torres
Publisher : World Scientific Publishing Company
Page : 280 pages
File Size : 40,7 Mb
Release : 2015-03-19
Category : Mathematics
ISBN : 9781783266425

Get Book

Computational Methods In The Fractional Calculus Of Variations by Ricardo Almeida,Shakoor Pooseh,Delfim F M Torres Pdf

This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.

Introduction to the Fractional Calculus of Variations

Agnieszka B Malinowska,Delfim F M Torres
Introduction to the Fractional Calculus of Variations Book PDF

Author : Agnieszka B Malinowska,Delfim F M Torres
Publisher : World Scientific Publishing Company
Page : 292 pages
File Size : 42,6 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9781848169685

Get Book

Introduction to the Fractional Calculus of Variations by Agnieszka B Malinowska,Delfim F M Torres Pdf

This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler–Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV. The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.

Optimal Control Via Nonsmooth Analysis

Philip Daniel Loewen
Optimal Control Via Nonsmooth Analysis Book PDF

Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 44,8 Mb
Release : 1993
Category : Control theory
ISBN : 0821869965

Get Book

Optimal Control Via Nonsmooth Analysis by Philip Daniel Loewen Pdf

This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Fractional Dynamics in Natural Phenomena and Advanced Technologies

Dumitru Baleanu,Jordan Hristov
Fractional Dynamics in Natural Phenomena and Advanced Technologies Book PDF

Author : Dumitru Baleanu,Jordan Hristov
Publisher : Cambridge Scholars Publishing
Page : 290 pages
File Size : 46,8 Mb
Release : 2024-01-29
Category : Juvenile Nonfiction
ISBN : 9781527552777

Get Book

Fractional Dynamics in Natural Phenomena and Advanced Technologies by Dumitru Baleanu,Jordan Hristov Pdf

This book addresses different applied problems in order to demonstrate the feasibility of fractional calculus’ use, irrespective of the type of memory kernels used, to model varieties of natural phenomena and new processes emerging in advanced technologies. In this context, the book’s focus is on modelling, adequate results, and interpretations, rather than theorems and proofs. The book includes a total of 12 chapters, representing various aspects of applied fractional modelling and covering important issues in modern technologies to provide a better understanding of applications of fractional calculus in applied modelling. The book will be a versatile source of information for undergraduate and graduate students, and for scientists involved in modelling of nonlinear and hereditary phenomena.

Outliers in Control Engineering

Paweł D. Domański,YangQuan Chen,Maciej Ławryńczuk
Outliers in Control Engineering Book PDF

Author : Paweł D. Domański,YangQuan Chen,Maciej Ławryńczuk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 272 pages
File Size : 48,7 Mb
Release : 2022-03-07
Category : Technology & Engineering
ISBN : 9783110729122

Get Book

Outliers in Control Engineering by Paweł D. Domański,YangQuan Chen,Maciej Ławryńczuk Pdf

Outliers play an important, though underestimated, role in control engineering. Traditionally they are unseen and neglected. In opposition, industrial practice gives frequent examples of their existence and their mostly negative impacts on the control quality. The origin of outliers is never fully known. Some of them are generated externally to the process (exogenous), like for instance erroneous observations, data corrupted by control systems or the effect of human intervention. Such outliers appear occasionally with some unknow probability shifting real value often to some strange and nonsense value. They are frequently called deviants, anomalies or contaminants. In most cases we are interested in their detection and removal. However, there exists the second kind of outliers. Quite often strange looking data observations are not artificial data occurrences. They may be just representatives of the underlying generation mechanism being inseparable internal part of the process (endogenous outliers). In such a case they are not wrong and should be treated with cautiousness, as they may include important information about the dynamic nature of the process. As such they cannot be neglected nor simply removed. The Outlier should be detected, labelled and suitably treated. These activities cannot be performed without proper analytical tools and modeling approaches. There are dozens of methods proposed by scientists, starting from Gaussian-based statistical scoring up to data mining artificial intelligence tools. The research presented in this book presents novel approach incorporating non-Gaussian statistical tools and fractional calculus approach revealing new data analytics applied to this important and challenging task. The proposed book includes a collection of contributions addressing different yet cohesive subjects, like dynamic modelling, classical control, advanced control, fractional calculus, statistical analytics focused on an ultimate goal: robust and outlier-proof analysis. All studied problems show that outliers play an important role and classical methods, in which outlier are not taken into account, do not give good results. Applications from different engineering areas are considered such as semiconductor process control and monitoring, MIMO peltier temperature control and health monitoring, networked control systems, and etc.

Fractional Order Analysis

Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
Fractional Order Analysis Book PDF

Author : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 45,7 Mb
Release : 2020-08-06
Category : Mathematics
ISBN : 9781119654230

Get Book

Fractional Order Analysis by Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana Pdf

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

Fractional Dynamics

Joseph Klafter,S. C. Lim,Ralf Metzler
Fractional Dynamics Book PDF

Author : Joseph Klafter,S. C. Lim,Ralf Metzler
Publisher : World Scientific
Page : 530 pages
File Size : 44,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814340595

Get Book

Fractional Dynamics by Joseph Klafter,S. C. Lim,Ralf Metzler Pdf

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Advances in Non-Integer Order Calculus and Its Applications

Agnieszka B. Malinowska,Dorota Mozyrska,Łukasz Sajewski
Advances in Non Integer Order Calculus and Its Applications Book PDF

Author : Agnieszka B. Malinowska,Dorota Mozyrska,Łukasz Sajewski
Publisher : Springer
Page : 307 pages
File Size : 46,9 Mb
Release : 2019-04-17
Category : Technology & Engineering
ISBN : 9783030173449

Get Book

Advances in Non-Integer Order Calculus and Its Applications by Agnieszka B. Malinowska,Dorota Mozyrska,Łukasz Sajewski Pdf

This book provides an overview of some recent findings in the theory and applications of non-integer order systems. Discussing topics ranging from the mathematical foundations to technical applications of continuous-time and discrete-time fractional calculus, it includes 22 original research papers and is subdivided into four parts: • Mathematical Foundations • Approximation, Modeling and Simulations • Fractional Systems Analysis and Control • Applications The papers were selected from those presented at the 10th International Conference of Non-integer Order Calculus and its Applications, which was held at the Bialystok University of Technology, Poland, September 20–21, 2018. Thanks to the broad spectrum of topics covered, the book is suitable for researchers from applied mathematics and engineering. It is also a valuable resource for graduate students, as well as for scholars looking for new mathematical tools.

Fractional Derivatives with Mittag-Leffler Kernel

José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Fractional Derivatives with Mittag Leffler Kernel Book PDF

Author : José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Publisher : Springer
Page : 341 pages
File Size : 48,6 Mb
Release : 2019-02-13
Category : Technology & Engineering
ISBN : 9783030116620

Get Book

Fractional Derivatives with Mittag-Leffler Kernel by José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar Pdf

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

Methods of Mathematical Modelling

Harendra Singh,Devendra Kumar,Dumitru Baleanu
Methods of Mathematical Modelling Book PDF

Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
Publisher : CRC Press
Page : 255 pages
File Size : 46,5 Mb
Release : 2019-09-17
Category : Mathematics
ISBN : 9781000596786

Get Book

Methods of Mathematical Modelling by Harendra Singh,Devendra Kumar,Dumitru Baleanu Pdf

This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications