Nonlocal And Fractional Operators
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Nonlocal And Fractional Operators
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Author : Luisa Beghin
language : en
Publisher: Springer Nature
Release Date : 2021-07-23
Nonlocal And Fractional Operators written by Luisa Beghin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-23 with Mathematics categories.
The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists and applied scientists interested in the various aspects of fractional calculus.
Nonlocal Nonlinear Fractional Order Boundary Value Problems
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Author : Bashir Ahmad
language : en
Publisher: World Scientific
Release Date : 2021-04-06
Nonlocal Nonlinear Fractional Order Boundary Value Problems written by Bashir Ahmad and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-06 with Mathematics categories.
There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
Variational Methods For Nonlocal Fractional Problems
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Author : Giovanni Molica Bisci
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-11
Variational Methods For Nonlocal Fractional Problems written by Giovanni Molica Bisci 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 2016-03-11 with Mathematics categories.
A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
Fractional Calculus And Fractional Differential Equations
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Author : Varsha Daftardar-Gejji
language : en
Publisher: Springer
Release Date : 2019-08-10
Fractional Calculus And Fractional Differential Equations written by Varsha Daftardar-Gejji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-10 with Mathematics categories.
This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Fractional Operators With Constant And Variable Order With Application To Geo Hydrology
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Author : Abdon Atangana
language : en
Publisher: Academic Press
Release Date : 2017-09-19
Fractional Operators With Constant And Variable Order With Application To Geo Hydrology written by Abdon Atangana and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.
Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author's analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution. - Proposes new aquifer derivatives for leaky, confined and unconfined formations - Presents useful aids for applied scientists and engineers seeking to solve complex problems that cannot be handled using constant fractional order derivatives - Provides a real physical interpretation of operators relevant to groundwater flow problems - Models both fractional and variable order derivatives, presented together with uncertainties analysis
New Developments In The Analysis Of Nonlocal Operators
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Author : Donatella Danielli
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21
New Developments In The Analysis Of Nonlocal Operators written by Donatella Danielli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28–30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance. The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.
Fractional Differential Equations
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Author : Igor Podlubny
language : en
Publisher: Elsevier
Release Date : 1998-10-27
Fractional Differential Equations written by Igor Podlubny and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-27 with Mathematics categories.
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Fuzzy Fractional Differential Operators And Equations
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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2020-06-15
Fuzzy Fractional Differential Operators And Equations written by Tofigh Allahviranloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-15 with Technology & Engineering categories.
This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.
The Fractional Laplacian
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Author : Wenxiong Chen
language : en
Publisher: World Scientific
Release Date : 2020-06-09
The Fractional Laplacian written by Wenxiong Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Mathematics categories.
This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.