Numerical Treatment And Analysis Of Time Fractional Evolution Equations

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Numerical Treatment And Analysis Of Time Fractional Evolution Equations

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Author : Bangti Jin
language : en
Publisher:
Release Date : 2023

Numerical Treatment And Analysis Of Time Fractional Evolution Equations written by Bangti Jin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.

Numerical Treatment And Analysis Of Time Fractional Evolution Equations

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Author : Bangti Jin
language : en
Publisher: Springer Nature
Release Date : 2023-02-26

Numerical Treatment And Analysis Of Time Fractional Evolution Equations written by Bangti Jin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-26 with Mathematics categories.

This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.

Fractional Evolution Equations And Inclusions

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Author : Yong Zhou
language : en
Publisher: Academic Press
Release Date : 2016-02-05

Fractional Evolution Equations And Inclusions written by Yong Zhou and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Mathematics categories.

Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature

Theory Of Fractional Evolution Equations

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Author : Yong Zhou
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-21

Theory Of Fractional Evolution Equations written by Yong Zhou 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 2022-03-21 with Mathematics categories.

Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.

Nonautonomous Fractional Evolution Equations

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Author : Yong Zhou
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Nonautonomous Fractional Evolution Equations written by Yong Zhou 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 2024-07-01 with Mathematics categories.

Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.

Subordination Principle For Fractional Evolution Equations

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Author : E. Bazhlekova
language : en
Publisher:
Release Date : 1999

Subordination Principle For Fractional Evolution Equations written by E. Bazhlekova and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Mathematical And Numerical Analysis Of Nonlinear Evolution Equations

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Author : Carlo Bianca
language : en
Publisher: Mdpi AG
Release Date : 2020-10-02

Mathematical And Numerical Analysis Of Nonlinear Evolution Equations written by Carlo Bianca and has been published by Mdpi AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.

The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schrödinger equation, and Cahn-Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.

Evolution Equations

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Author : Kaïs Ammari
language : en
Publisher: Cambridge University Press
Release Date : 2018

Evolution Equations written by Kaïs Ammari 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 with Mathematics categories.

The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Fractional Dispersive Models And Applications

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Author : Panayotis G. Kevrekidis
language : en
Publisher: Springer Nature
Release Date :

Fractional Dispersive Models And Applications written by Panayotis G. Kevrekidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Theory And Numerical Approximations Of Fractional Integrals And Derivatives

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Author : Changpin Li
language : en
Publisher: SIAM
Release Date : 2019-10-31

Theory And Numerical Approximations Of Fractional Integrals And Derivatives written by Changpin Li and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-31 with Mathematics categories.

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus, provides a detailed treatment of existing numerical approximations, and presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.