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Fractional S P Des Theory Numerics And Optimal Control

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Fractional S P Des Theory Numerics And Optimal Control

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Author : Wilfried Grecksch
language : en
Publisher: World Scientific
Release Date : 2025-06-03

Fractional S P Des Theory Numerics And Optimal Control written by Wilfried Grecksch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-03 with Mathematics categories.

Recent breakthroughs in volatility modelling have brought fractional stochastic calculus to a groundbreaking position. Readers of Fractional S(P)DEs will find a unique and comprehensive overview encompassing the theory and the numerics of both ordinary and partial differential equations (SDEs and SPDEs, respectively), driven by fractional Brownian motion.Within this book, both differential equations are considered with fractional noise, while also considering fractional derivatives in the case of SPDEs. Three primary aspects are pursued: Theory and numerics for rough SPDEs; Optimal control of both SDEs and SPDEs driven by fractional Brownian motions (and their applications); And numerics for time-fractional SPDEs driven by both Gaussian and non-Gaussian noises.This series of complementary articles, compiled by two internationally renowned scientists, is united by a common application-oriented view of fractional Brownian motion and its stochastic calculus. As such, this book will be particularly useful for mathematicians working in the fields of stochastics applied in Finance and Natural Sciences, as well as those preparing courses on advanced stochastic processes.

Fixed Point Theory And Fractional Calculus

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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-05-10

Fixed Point Theory And Fractional Calculus written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Fractional S P Des Theory Numerics And Optimal Control

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Author : LISEI
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-07-03

Fractional S P Des Theory Numerics And Optimal Control written by LISEI 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 2025-07-03 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.

Numerical Analysis 1993

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Author : D.F. Griffiths
language : en
Publisher: CRC Press
Release Date : 2020-10-07

Numerical Analysis 1993 written by D.F. Griffiths and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.

This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.

Generalized Fractional Calculus And Applications

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Author : Virginia S Kiryakova
language : en
Publisher: CRC Press
Release Date : 1993-12-27

Generalized Fractional Calculus And Applications written by Virginia S Kiryakova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-27 with Mathematics categories.

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.

Equations Involving Malliavin Calculus Operators

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Author : Tijana Levajković
language : en
Publisher: Springer
Release Date : 2017-08-31

Equations Involving Malliavin Calculus Operators written by Tijana Levajković and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Mathematics categories.

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed. Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied – applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems."

Propagation Of A Curved Shock And Nonlinear Ray Theory

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Author : Prasad
language : en
Publisher: CRC Press
Release Date : 1993-09-27

Propagation Of A Curved Shock And Nonlinear Ray Theory written by Prasad and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-27 with Mathematics categories.

Phoolan Prasad's book contains theoretical developments in the study of the propagation of a curved nonlinear wave front and shock front, particularly in the caustic region. It should be an invaluable reference source for researchers in nonlinear waves; fluid dynamics (especially gas dynamics); mathematical physics; aeronautical, chemical and mechanical engineering.

Variational Methods In Lorentzian Geometry

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Author : Antonio Masiello
language : en
Publisher: Routledge
Release Date : 2017-10-05

Variational Methods In Lorentzian Geometry written by Antonio Masiello and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Mathematics categories.

Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.

A Method For Computing Unsteady Flows In Porous Media

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Author : R Raghavan
language : en
Publisher: Routledge
Release Date : 2017-11-22

A Method For Computing Unsteady Flows In Porous Media written by R Raghavan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Self-contained and concise, this Research Note provides a basis to study unsteady flow in saturated porous media. It provides for the development of algorithms that examine three-dimensional flows subject to complicated boundary conditions that are a natural consequence of flow in geological systems. A new way to understand the flow in porous media is presented. The authors pay attention to computational considerations, and options for developing codes are addressed. The note consists of five chapters: the first is introductory; the second and third are devoted to showing how one arrives at the solutions of interest; the fourth chapter presents various reformulations to aid computations and presents a few illustrative examples; the fifth chapter is a natural progression of the first four chapters to more complicated visualizations of flow in porous media.

Fractional S P Des Theory Numerics And Optimal Control

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