Fractional Calculus For Scientists And Engineers
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Fractional Calculus For Scientists And Engineers
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Author : Manuel Duarte Ortigueira
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-02
Fractional Calculus For Scientists And Engineers written by Manuel Duarte Ortigueira 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 2011-06-02 with Technology & Engineering categories.
This book gives a practical overview of Fractional Calculus as it relates to Signal Processing
Handbook Of Fractional Calculus For Engineering And Science
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2022-02-16
Handbook Of Fractional Calculus For Engineering And Science written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-16 with Mathematics categories.
Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
Fractional Derivatives With Mittag Leffler Kernel
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Author : José Francisco Gómez
language : en
Publisher: Springer
Release Date : 2019-02-13
Fractional Derivatives With Mittag Leffler Kernel written by José Francisco Gómez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-13 with Technology & Engineering categories.
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.
Advances In Fractional Calculus
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Author : J. Sabatier
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
Advances In Fractional Calculus written by J. Sabatier 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 2007-07-28 with Technology & Engineering categories.
In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Advanced Applications Of Fractional Differential Operators To Science And Technology
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Author : Matouk, Ahmed Ezzat
language : en
Publisher: IGI Global
Release Date : 2020-04-24
Advanced Applications Of Fractional Differential Operators To Science And Technology written by Matouk, Ahmed Ezzat and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-24 with Mathematics categories.
Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques.
Fractional Derivatives For Physicists And Engineers
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Author : Vladimir V. Uchaikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-09
Fractional Derivatives For Physicists And Engineers written by Vladimir V. Uchaikin 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 2013-07-09 with Science categories.
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.
Linear Fractional Diffusion Wave Equation For Scientists And Engineers
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Author : Yuriy Povstenko
language : en
Publisher: Birkhäuser
Release Date : 2015-07-03
Linear Fractional Diffusion Wave Equation For Scientists And Engineers written by Yuriy Povstenko and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-03 with Mathematics categories.
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.
Special Functions In Fractional Calculus And Engineering
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2023-06-29
Special Functions In Fractional Calculus And Engineering written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-29 with Technology & Engineering categories.
Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.
Fractional Derivatives For Physicists And Engineers
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Author : Vladimir Vasilʹevich Uchaĭkin
language : en
Publisher:
Release Date : 2013
Fractional Derivatives For Physicists And Engineers written by Vladimir Vasilʹevich Uchaĭkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic books categories.
Mathematical Methods In Science And Engineering
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Author : Selcuk S. Bayin
language : en
Publisher: John Wiley & Sons
Release Date : 2018-03-27
Mathematical Methods In Science And Engineering written by Selcuk S. Bayin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-27 with Education categories.
A Practical, Interdisciplinary Guide to Advanced Mathematical Methods for Scientists and Engineers Mathematical Methods in Science and Engineering, Second Edition, provides students and scientists with a detailed mathematical reference for advanced analysis and computational methodologies. Making complex tools accessible, this invaluable resource is designed for both the classroom and the practitioners; the modular format allows flexibility of coverage, while the text itself is formatted to provide essential information without detailed study. Highly practical discussion focuses on the “how-to” aspect of each topic presented, yet provides enough theory to reinforce central processes and mechanisms. Recent growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance to expand advanced mathematical methods beyond theoretical physics. This book is written with this multi-disciplinary group in mind, emphasizing practical solutions for diverse applications and the development of a new interdisciplinary science. Revised and expanded for increased utility, this new Second Edition: Includes over 60 new sections and subsections more useful to a multidisciplinary audience Contains new examples, new figures, new problems, and more fluid arguments Presents a detailed discussion on the most frequently encountered special functions in science and engineering Provides a systematic treatment of special functions in terms of the Sturm-Liouville theory Approaches second-order differential equations of physics and engineering from the factorization perspective Includes extensive discussion of coordinate transformations and tensors, complex analysis, fractional calculus, integral transforms, Green's functions, path integrals, and more Extensively reworked to provide increased utility to a broader audience, this book provides a self-contained three-semester course for curriculum, self-study, or reference. As more scientific disciplines begin to lean more heavily on advanced mathematical analysis, this resource will prove to be an invaluable addition to any bookshelf.