Fractal Calculus And Its Applications F Calculus
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Applications Of Fractional Calculus In Physics
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Author : Rudolf Hilfer
language : en
Publisher: World Scientific
Release Date : 2000-03-02
Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-02 with Science categories.
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.
Fractal Calculus And Its Applications
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Author : Alireza Khalili Golmankhaneh
language : en
Publisher:
Release Date : 2022
Fractal Calculus And Its Applications written by Alireza Khalili Golmankhaneh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Fractal analysis categories.
"The first book to introduce the theory and applications of fractal calculus and provide a basis for research and development of this framework"--
Fractional Calculus And Fractional Processes With Applications To Financial Economics
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Author : Hasan Fallahgoul
language : en
Publisher: Academic Press
Release Date : 2016-10-06
Fractional Calculus And Fractional Processes With Applications To Financial Economics written by Hasan Fallahgoul and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-06 with Mathematics categories.
Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization. - Provides the necessary background for the book's content as applied to financial economics - Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives
Fractal Calculus And Its Applications F Calculus
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Author : Alireza Khalili Golmankhaneh
language : en
Publisher: World Scientific
Release Date : 2022-08-29
Fractal Calculus And Its Applications F Calculus written by Alireza Khalili Golmankhaneh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-29 with Mathematics categories.
Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.
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.
Stochastic Calculus For Fractional Brownian Motion And Applications
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Author : Francesca Biagini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Stochastic Calculus For Fractional Brownian Motion And Applications written by Francesca Biagini 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 2008-02-17 with Mathematics categories.
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for fBm. The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.
Functional Fractional Calculus For System Identification And Controls
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Author : Shantanu Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-26
Functional Fractional Calculus For System Identification And Controls written by Shantanu Das 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 2007-09-26 with Technology & Engineering categories.
In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
Fractional Dynamics
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Author : Vasily E. Tarasov
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04
Fractional Dynamics written by Vasily E. Tarasov 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 2011-01-04 with Science categories.
"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.
New Trends In Nanotechnology And Fractional Calculus Applications
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Author : Dumitru Baleanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-14
New Trends In Nanotechnology And Fractional Calculus Applications written by Dumitru Baleanu 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 2010-03-14 with Technology & Engineering categories.
In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.
Introduction To The Fractional Calculus Of Variations
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Author : Delfim F M Torres
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-09-14
Introduction To The Fractional Calculus Of Variations written by Delfim F M Torres and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
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./a