Nonlocal and Fractional Operators, Ahmadieh Khanesar, Mojtaba Kaynak, Okyay Kayacan, Erdal

Автор: Beghin Luisa, Mainardi Francesco, Garrappa Roberto
Название: Nonlocal and Fractional Operators
ISBN: 3030692353 ISBN-13(EAN): 9783030692353
Издательство: Springer
Цена: 19564.00 р.
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Описание: The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus.

Автор: Bashir Ahmad, Sotiris K Ntouyas
Название: Nonlocal Nonlinear Fractional-order Boundary Value Problems
ISBN: 9811230404 ISBN-13(EAN): 9789811230400
Издательство: World Scientific Publishing
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Описание:

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.

Автор: Peter William Egolf, Kolumban Hutter
Название: Nonlinear, Nonlocal and Fractional Turbulence
ISBN: 3030260321 ISBN-13(EAN): 9783030260323
Издательство: Springer
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Описание: Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure.

Автор: Palatucci Giampiero, Kuusi Tuomo
Название: Recent Developments in Nonlocal Theory
ISBN: 3110571552 ISBN-13(EAN): 9783110571554
Издательство: Walter de Gruyter
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Описание:

This edited volume aims at giving an overview of recent advances in the theory and applications of Partial Differential Equations and energy functionals related to the fractional Laplacian operator as well as to more general integro-differential operators with singular kernel of fractional differentiability.
After being investigated firstly in Potential Theory and Harmonic Analysis, fractional operators defined via singular integral are nowadays riveting great attention in different research fields related to Partial Differential Equations with nonlocal terms, since they naturally arise in many different contexts, as for instance, dislocations in crystals, nonlocal minimal surfaces, the obstacle problem, the fractional Yamabe problem, and many others.
Much progress has been made during the last years, and this edited volume presents a valuable update to a wide community interested in these topics.

Автор: Jos? M. Maz?n; Julio Daniel Rossi; J. Juli?n Toled
Название: Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets
ISBN: 3030062422 ISBN-13(EAN): 9783030062422
Издательство: Springer
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Описание: This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.

Автор: Claudia Bucur; Enrico Valdinoci
Название: Nonlocal Diffusion and Applications
ISBN: 3319287389 ISBN-13(EAN): 9783319287386
Издательство: Springer
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Описание: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrodinger equations are given.

Автор: Andrey Anatoljevich Grib; Waldyr Alves Rodrigues J
Название: Nonlocality in Quantum Physics
ISBN: 1461371228 ISBN-13(EAN): 9781461371229
Издательство: Springer
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Описание: The nonlocality phenomena exhibited by entangled quantum systems are certainly one of the most extraordinary aspects of quantum theory. Recent results on cryptography, quantum bit commitment, quantum erasers and teleportation are also presented and discussed.