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Author: Jagdev Singh
Publisher: Frontiers Media SA
ISBN: 2889663043
Category : Science
Languages : en
Pages : 172
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Book Description
This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
Author: Jagdev Singh
Publisher: Frontiers Media SA
ISBN: 2889663043
Category : Science
Languages : en
Pages : 172
Get Book
Book Description
This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
Author: Boling Guo
Publisher: World Scientific
ISBN: 9814667064
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau–Lifshitz equations and fractional Ginzburg–Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs. Contents:Physics BackgroundFractional Calculus and Fractional Differential EquationsFractional Partial Differential EquationsNumerical Approximations in Fractional CalculusNumerical Methods for the Fractional Ordinary Differential EquationsNumerical Methods for Fractional Partial Differential Equations Readership: Graduate students and researchers in mathematical physics, numerical analysis and computational mathematics. Key Features:This book covers the fundamentals of this field, especially for the beginnersThe book covers new trends and results in this fieldThe book covers numerical results, which will be of broad interests to researchersKeywords:Fractional Partial Differential Equations;Numerical Solutions
Author: Dumitru Baleanu
Publisher: Cambridge Scholars Publishing
ISBN: 1527552772
Category : Juvenile Nonfiction
Languages : en
Pages : 290
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Book Description
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.
Author: Vasily E. Tarasov
Publisher: Springer Science & Business Media
ISBN: 3642140033
Category : Science
Languages : en
Pages : 504
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Book Description
"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.
Author: Kai Diethelm
Publisher: Springer
ISBN: 3642145744
Category : Mathematics
Languages : en
Pages : 247
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Book Description
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.
Author: Rudolf Hilfer
Publisher: World Scientific
ISBN: 9814496200
Category : Science
Languages : en
Pages : 473
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Book Description
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
Author: Anatoly Kochubei
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110571668
Category : Mathematics
Languages : en
Pages : 528
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Book Description
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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Author: Igor Podlubny
Publisher: Elsevier
ISBN: 0080531989
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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
Author: Dumitru Baleanu
Publisher: Frontiers Media SA
ISBN: 2889459586
Category :
Languages : en
Pages : 93
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Book Description
Author: Juan J. Nieto
Publisher: MDPI
ISBN: 3039217321
Category : Mathematics
Languages : en
Pages : 172
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Book Description
Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.
