Special Functions Of Fractional Calculus Applications To Diffusion And Random Search Processes
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Special Functions Of Fractional Calculus Applications To Diffusion And Random Search Processes
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Author : Trifce Sandev
language : en
Publisher: World Scientific
Release Date : 2022-10-07
Special Functions Of Fractional Calculus Applications To Diffusion And Random Search Processes written by Trifce Sandev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Mathematics categories.
This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Advances In Fractional Calculus
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Author : J. Juan Rosales García
language : en
Publisher: Springer Nature
Release Date : 2025-06-02
Advances In Fractional Calculus written by J. Juan Rosales García and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-02 with Technology & Engineering categories.
This book offers a timely snapshot of research in fractional calculus. Based on peer-reviewed, selected contributions to the 6th Mexican Workshop on Fractional Calculus (MWFC), held on October 9-11, 2024 at the University of Guanajuato, in León, Guanajuato México, it offers extensive information on current trends. Chapters cover advances on fractional derivatives and integrals, and fractional differential equations, together with interdisciplinary applications of fractional calculus to real-world scenarios, chaotic and complex systems, and control.
Target Search Problems
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Author : Denis Grebenkov
language : en
Publisher: Springer Nature
Release Date : 2024-12-26
Target Search Problems written by Denis Grebenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-26 with Science categories.
This book presents cutting-edge research addressing the mathematical models used to tackle the "Target problem" as it manifests itself in a wide range of disciplines. Leading international experts from around the world describe a variety of different approaches to this truly multidisciplinary topic. Recent years have witnessed a substantial and still growing interest in understanding the general "Target problem". This encompasses a wide range of different situations in which some "agents" perform a deterministic or stochastic motion to search for a certain immobile or mobile "target". Such problems arise in many disciplines: to name but a few, computer science, the evolution of stock markets, biochemistry, bio-medicine, evolutionary games, as well as diverse areas of physics. This book with its up-to-date collection of chapters authored by leading experts in these and other fields, provides a comprehensive and complete picture in broadlyaccessible language. The book will naturally serve as a source of inspiration for further research, as well as facilitating a cross-fertilization of approaches, ideas, and research directions.
Fractional Diffusion Equations And Anomalous Diffusion
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Author : Luiz Roberto Evangelista
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Fractional Diffusion Equations And Anomalous Diffusion written by Luiz Roberto Evangelista and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-25 with Mathematics categories.
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Stochastic Models For Fractional Calculus
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Author : Mark M. Meerschaert
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Stochastic Models For Fractional Calculus written by Mark M. Meerschaert and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.
Fractional Calculus Theory And Applications
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Author : Francesco Mainardi
language : en
Publisher: MDPI
Release Date : 2018-09-20
Fractional Calculus Theory And Applications written by Francesco Mainardi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.
This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics
Mathematical Methods In Engineering
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Author : K. Tas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-25
Mathematical Methods In Engineering written by K. Tas 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 2007-11-25 with Technology & Engineering categories.
This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.
Fractional Diffusion And Wave Equations
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Author : Yong Zhou
language : en
Publisher: Springer Nature
Release Date : 2024-11-05
Fractional Diffusion And Wave Equations written by Yong Zhou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.
This monograph delves into the theory of time-fractional diffusion and wave equations, presenting a comprehensive exploration of recent advancements in the field. Key topics include well-posedness, regularity, and approximate controllability of Cauchy problems, as well as the existence and regularity of terminal value problems. Detailed examples illustrate the applications of these equations, demonstrating their practical relevance. The content is rooted in research conducted by the author and other experts over the past five years, offering a thorough foundation for further study. This work is an invaluable resource for researchers, graduate students, and PhD candidates in the fields of differential equations, applied analysis, and related areas.
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
Special Functions For Applied Scientists
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-13
Special Functions For Applied Scientists written by A.M. Mathai 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 2008-02-13 with Science categories.
Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introduction to statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed. Their applications to reaction-diffusion problems in physics, input-output analysis, and Mittag-Leffler stochastic processes are developed. Chapter 3 deals with q-hyper-geometric or basic hypergeometric functions. Chapter 4 covers basic hypergeometric functions and Ramanujan's work on elliptic and theta functions. Chapter 5 examines the topic of special functions and Lie groups. Chapters 6 to 9 are devoted to applications of special functions. Applications to stochastic processes, geometric infinite divisibility of random variables, Mittag-Leffler processes, alpha-Laplace processes, density estimation, order statistics and astrophysics problems, are dealt with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis. An introduction to wavelet analysis is given. Chapter 11 deals with the Jacobians of matrix transformations. Various types of matrix transformations and the associated Jacobians are provided. Chapter 12 is devoted to the discussion of functions of matrix argument in the real case. Functions of matrix argument and the pathway models along with their applications are discussed.