Fractional Calculus Models And Numerical Methods
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Fractional Calculus
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Author : Dumitru Baleanu
language : en
Publisher: World Scientific
Release Date : 2012
Fractional Calculus written by Dumitru Baleanu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This title 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.
Fractional Calculus Models And Numerical Methods Second Edition
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Author : Juan J Trujillo
language : en
Publisher: World Scientific
Release Date : 2016-09-15
Fractional Calculus Models And Numerical Methods Second Edition written by Juan J Trujillo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-15 with Mathematics categories.
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 Calculus
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Author : Dumitru Baleanu
language : en
Publisher:
Release Date : 2016
Fractional Calculus written by Dumitru Baleanu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electronic books categories.
"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."--Publisher's website.
Fractional Calculus Models And Numerical Methods
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Author : Dumitru Baleanu
language : en
Publisher: World Scientific
Release Date : 2012-01-27
Fractional Calculus Models And Numerical Methods written by Dumitru Baleanu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-27 with Mathematics categories.
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.
Fractional Calculus
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Author : Dumitru Baleanu
language : en
Publisher: Series on Complexity, Nonlinearity, and Chaos
Release Date : 2016-09-19
Fractional Calculus written by Dumitru Baleanu and has been published by Series on Complexity, Nonlinearity, and Chaos this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Fractional calculus categories.
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.
Numerical Methods For Fractional Calculus
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Author : Changpin Li
language : en
Publisher: CRC Press
Release Date : 2015-05-19
Numerical Methods For Fractional Calculus written by Changpin Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-19 with Mathematics categories.
Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs.The book introduces the basic definitions and propertie
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering
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Author : Oscar Castillo
language : en
Publisher: Springer Nature
Release Date : 2025-06-01
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering written by Oscar Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-01 with Technology & Engineering categories.
This book includes studies that give mathematical solution methods and mathematical modeling to support these methods for solving problems in the current application area of engineering, as well as studies that include solutions for problems that are also related to current life areas. In this book, some current problems in the field of mathematics and engineering, solutions to solve these problems and existing engineering methods for these problems are included. Basically, machinery, chemistry, electronics, computers, construction, environment, etc. studies in both the application and theoretical fields of mathematics are needed to solve optimization, modeling, encryption methods and thermal problems that are currently encountered in engineering fields. In this book, some current problems are presented and related theoretical and applied mathematical studies are included.
Applications In Engineering Life And Social Sciences Part B
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Author : Dumitru Bǎleanu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-04-01
Applications In Engineering Life And Social Sciences Part B written by Dumitru Bǎleanu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-01 with Mathematics categories.
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.
Viscoelastic Subdiffusive Flows
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Author : Helen Wilson
language : en
Publisher: Springer Nature
Release Date : 2024-12-31
Viscoelastic Subdiffusive Flows written by Helen Wilson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Technology & Engineering categories.
This book discusses the dynamical and rheological properties of high molecular weight entangled polymer melts, commonly known as viscoelastic subdiffusive fluids. Unlike dilute liquids, these materials exhibit molecular transport within a sublinear regime, meaning the timescale of diffusive transport is sublinear. The text emphasizes the potential of fractional calculus in modeling these fluids and introduces a novel fractional model to investigate regions of spatiotemporal instability in channel flows. At the microscale, the entanglement of polymer chains leads to localized, non-homogeneous regions with increased viscosity, which manifest as spatiotemporal macrostructures at the macroscale. To capture these macrostructures within the flow, direct numerical simulations are employed using a newly developed, physically realizable structure tensor, contributing to a deeper understanding of this complex class of fluids.
Discontinuity And Complexity In Nonlinear Physical Systems
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Author : J. A. Tenreiro Machado
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-04
Discontinuity And Complexity In Nonlinear Physical Systems written by J. A. Tenreiro Machado and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-04 with Technology & Engineering categories.
Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.