Efficient Numerical Methods For Fractional Differential Equations And Their Analytical Background

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Fractional Differential Equations

Author : Igor Podlubny
Publisher : Elsevier
ISBN 13 : 0080531989
Total Pages : 366 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Fractional Differential Equations by : Igor Podlubny

Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Analysis of Fractional Differential Equations

Author : Kai Diethelm
Publisher : Springer
ISBN 13 : 3642145744
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Introduction to Fractional Differential Equations

Author : Constantin Milici
Publisher : Springer
ISBN 13 : 3030008959
Total Pages : 199 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Introduction to Fractional Differential Equations by : Constantin Milici

Download or read book Introduction to Fractional Differential Equations written by Constantin Milici and published by Springer. This book was released on 2018-10-28 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion

Download High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion PDF Online Free

Author : Weihua Deng
Publisher : World Scientific
ISBN 13 : 9813142227
Total Pages : 295 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion by : Weihua Deng

Download or read book High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion written by Weihua Deng and published by World Scientific. This book was released on 2019-01-22 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

Fractional Calculus: Models And Numerical Methods

Author : Dumitru Baleanu
Publisher : World Scientific
ISBN 13 : 9814458635
Total Pages : 426 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Fractional Calculus: Models And Numerical Methods by : Dumitru Baleanu

Download or read book Fractional Calculus: Models And Numerical Methods written by Dumitru Baleanu and published by World Scientific. This book was released on 2012-01-27 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.

Numerical Solutions of Realistic Nonlinear Phenomena

Author : J. A. Tenreiro Machado
Publisher : Springer Nature
ISBN 13 : 3030371417
Total Pages : 231 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Numerical Solutions of Realistic Nonlinear Phenomena by : J. A. Tenreiro Machado

Download or read book Numerical Solutions of Realistic Nonlinear Phenomena written by J. A. Tenreiro Machado and published by Springer Nature. This book was released on 2020-02-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.

Fractional Diffusion Equations and Anomalous Diffusion

Author : Luiz Roberto Evangelista
Publisher : Cambridge University Press
ISBN 13 : 1108695035
Total Pages : 362 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Fractional Diffusion Equations and Anomalous Diffusion by : Luiz Roberto Evangelista

Download or read book Fractional Diffusion Equations and Anomalous Diffusion written by Luiz Roberto Evangelista and published by Cambridge University Press. This book was released on 2018-01-25 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

Intelligent Information and Database Systems

Author : Manh Thanh Le
Publisher : Springer Science & Business Media
ISBN 13 : 3642121446
Total Pages : 499 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Intelligent Information and Database Systems by : Manh Thanh Le

Download or read book Intelligent Information and Database Systems written by Manh Thanh Le and published by Springer Science & Business Media. This book was released on 2010-03-05 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2010 Asian Conference on Intelligent Information and Database Systems (ACIIDS) was the second event of the series of international scientific conferences for research and applications in the field of intelligent information and database systems. The aim of ACIIDS 2010 was to provide an international forum for scientific research in the technologies and applications of intelligent information, database systems and their applications. ACIIDS 2010 was co-organized by Hue University (Vietnam) and Wroclaw University of Technology (Poland) and took place in Hue city (Vietnam) during March 24–26, 2010. We received almost 330 papers from 35 countries. Each paper was peer reviewed by at least two members of the International Program Committee and International Reviewer Board. Only 96 best papers were selected for oral presentation and publi- tion in the two volumes of the ACIIDS 2010 proceedings. The papers included in the proceedings cover the following topics: artificial social systems, case studies and reports on deployments, collaborative learning, collaborative systems and applications, data warehousing and data mining, database management technologies, database models and query languages, database security and integrity,- business, e-commerce, e-finance, e-learning systems, information modeling and - quirements engineering, information retrieval systems, intelligent agents and mul- agent systems, intelligent information systems, intelligent internet systems, intelligent optimization techniques, object-relational DBMS, ontologies and information sharing, semi-structured and XML database systems, unified modeling language and unified processes, Web services and Semantic Web, computer networks and communication systems.

Automation 2019

Author : Roman Szewczyk
Publisher : Springer
ISBN 13 : 3030132730
Total Pages : 738 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Automation 2019 by : Roman Szewczyk

Download or read book Automation 2019 written by Roman Szewczyk and published by Springer. This book was released on 2019-02-15 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of papers presented at AUTOMATION2019, an international conference held in Warsaw from March 27 to 29, 2019. It discusses the radical technological changes occurring due to the INDUSTRY 4.0. To follow these changes, both scientists and engineers have to face the challenge of interdisciplinary approach directed at the development of cyber-physical systems. This approach encompasses interdisciplinary theoretical knowledge, numerical modelling and simulation as well as application of artificial intelligence techniques. Both software and physical devices are composed into systems that will increase production efficiency and resource savings. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems.

Fractional Calculus: Models And Numerical Methods (Second Edition)

Author : Juan J Trujillo
Publisher : World Scientific
ISBN 13 : 9813140054
Total Pages : 477 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Fractional Calculus: Models And Numerical Methods (Second Edition) by : Juan J Trujillo

Download or read book Fractional Calculus: Models And Numerical Methods (Second Edition) written by Juan J Trujillo and published by World Scientific. This book was released on 2016-09-15 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice.The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

Fractional Dynamical Systems: Methods, Algorithms and Applications

Author : Piotr Kulczycki
Publisher : Springer Nature
ISBN 13 : 3030899721
Total Pages : 398 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Fractional Dynamical Systems: Methods, Algorithms and Applications by : Piotr Kulczycki

Download or read book Fractional Dynamical Systems: Methods, Algorithms and Applications written by Piotr Kulczycki and published by Springer Nature. This book was released on 2022-01-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Analysis of Fractional Differential Equations

Author : Kai Diethelm
Publisher : Springer Science & Business Media
ISBN 13 : 3642145736
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer Science & Business Media. This book was released on 2010-09-03 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Fractional Derivatives for Physicists and Engineers

Author : Vladimir V. Uchaikin
Publisher : Springer Science & Business Media
ISBN 13 : 3642339115
Total Pages : 400 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fractional Derivatives for Physicists and Engineers by : Vladimir V. Uchaikin

Download or read book Fractional Derivatives for Physicists and Engineers written by Vladimir V. Uchaikin and published by Springer Science & Business Media. This book was released on 2013-07-09 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.

Numerical Solution of Ordinary Differential Equations

Author : Kendall Atkinson
Publisher : John Wiley & Sons
ISBN 13 : 1118164520
Total Pages : 272 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson

Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Time Delay Systems

Author : Tamás Insperger
Publisher : Springer
ISBN 13 : 3319534262
Total Pages : 359 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Time Delay Systems by : Tamás Insperger

Download or read book Time Delay Systems written by Tamás Insperger and published by Springer. This book was released on 2017-03-30 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.

Numerical Methods in Computational Finance

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
ISBN 13 : 1119719720
Total Pages : 551 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Numerical Methods in Computational Finance by : Daniel J. Duffy

Download or read book Numerical Methods in Computational Finance written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2022-03-14 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

Analytic Methods for Partial Differential Equations

Author : G. Evans
Publisher : Springer Science & Business Media
ISBN 13 : 1447103793
Total Pages : 308 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Analytic Methods for Partial Differential Equations by : G. Evans

Download or read book Analytic Methods for Partial Differential Equations written by G. Evans and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.