Fractional Calculus and Its Applications
Author : B. Ross
Publisher : Springer
Page : 391 pages
File Size : 48,92 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540699759
Author : B. Ross
Publisher : Springer
Page : 391 pages
File Size : 48,92 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540699759
Author : Virginia S Kiryakova
Publisher : CRC Press
Page : 412 pages
File Size : 34,63 MB
Release : 1993-12-27
Category : Mathematics
ISBN : 9780582219779
In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Author : J. Sabatier
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 46,41 MB
Release : 2007-07-28
Category : Technology & Engineering
ISBN : 1402060424
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.
Author : Hasan Fallahgoul
Publisher : Academic Press
Page : 120 pages
File Size : 23,62 MB
Release : 2016-10-06
Category : Mathematics
ISBN : 0128042842
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
Author : Devendra Kumar
Publisher : CRC Press
Page : 232 pages
File Size : 44,88 MB
Release : 2020-06-25
Category : Mathematics
ISBN : 9780429340567
This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.
Author : Dumitru Baleanu
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 21,76 MB
Release : 2010-03-14
Category : Technology & Engineering
ISBN : 9048132932
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.
Author : Rudolf Hilfer
Publisher : World Scientific
Page : 473 pages
File Size : 43,45 MB
Release : 2000-03-02
Category : Science
ISBN : 9814496200
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 : A.A. Kilbas
Publisher : Elsevier
Page : 550 pages
File Size : 26,92 MB
Release : 2006-02-16
Category : Mathematics
ISBN : 9780444518323
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Author : Santanu Saha Ray
Publisher : CRC Press
Page : 232 pages
File Size : 39,3 MB
Release : 2015-07-29
Category : Mathematics
ISBN : 149872728X
Introduces Novel Applications for Solving Neutron Transport EquationsWhile deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous way
Author : Richard Herrmann
Publisher : World Scientific
Page : 274 pages
File Size : 49,35 MB
Release : 2011
Category : Science
ISBN : 9814340243
Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in the subjects of classical mechanics, friction, damping, oscillations, group theory, quantum mechanics, nuclear physics, and hadron spectroscopy up to quantum field theory.