Fractional Calculus And Its Applications
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Fractional Calculus And Its Applications
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Author : B. Ross
language : en
Publisher: Springer
Release Date : 2006-11-15
Fractional Calculus And Its Applications written by B. Ross and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
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.
Theory And Applications Of Fractional Differential Equations
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Author : A.A. Kilbas
language : en
Publisher: Elsevier
Release Date : 2006-02-16
Theory And Applications Of Fractional Differential Equations written by A.A. Kilbas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-16 with Mathematics categories.
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.
Fractional Dynamics
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Author : Carlo Cattani
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-01-01
Fractional Dynamics written by Carlo Cattani 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 2015-01-01 with Mathematics categories.
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
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.
General Fractional Derivatives
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Author : Xiao-Jun Yang
language : en
Publisher: CRC Press
Release Date : 2019-05-10
General Fractional Derivatives written by Xiao-Jun Yang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
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
Local Fractional Integral Transforms And Their Applications
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Author : Xiao-Jun Yang
language : en
Publisher: Academic Press
Release Date : 2015-10-22
Local Fractional Integral Transforms And Their Applications written by Xiao-Jun Yang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. - Provides applications of local fractional Fourier Series - Discusses definitions for local fractional Laplace transforms - Explains local fractional Laplace transforms coupled with analytical methods
Fractional Calculus For Hydrology Soil Science And Geomechanics
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Author : Ninghu Su
language : en
Publisher: CRC Press
Release Date : 2020-11-02
Fractional Calculus For Hydrology Soil Science And Geomechanics written by Ninghu Su and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Science categories.
This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.