Fractional Diffusion And Wave Equations
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Fractional Diffusion And Wave Equations
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Author : Yong Zhou
language : en
Publisher:
Release Date : 2024
Fractional Diffusion And Wave Equations written by Yong Zhou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Integral equations categories.
Preface -- Introduction -- Preliminaries -- Well-posedness of Fractional Diffusion Equations -- Inverse Problems of Fractional Diffusion Equations -- Well-posedness and Regularity of Fractional Wave Equations -- Inverse Problems of Fractional Wave Equations -- References -- Index.
Fractals And Fractional Calculus In Continuum Mechanics
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Author : Alberto Carpinteri
language : en
Publisher: Springer
Release Date : 2014-05-04
Fractals And Fractional Calculus In Continuum Mechanics written by Alberto Carpinteri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.
The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
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.
Progress In Intelligent Decision Science
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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2021-01-29
Progress In Intelligent Decision Science 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 2021-01-29 with Technology & Engineering categories.
This book contains the topics of artificial intelligence and deep learning that do have much application in real-life problems. The concept of uncertainty has long been used in applied science, especially decision making and a logical decision must be made in the field of uncertainty or in the real-life environment that is formed and combined with vague concepts and data. The chapters of this book are connected to the new concepts and aspects of decision making with uncertainty. Besides, other chapters are involved with the concept of data mining and decision making under uncertain computations.
Advanced Mathematical Methods For Scientists And Engineers I
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Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender 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 2013-03-09 with Mathematics categories.
The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.
Linear Fractional Diffusion Wave Equation For Scientists And Engineers
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Author : Yuriy Povstenko
language : en
Publisher: Birkhäuser
Release Date : 2015-07-03
Linear Fractional Diffusion Wave Equation For Scientists And Engineers written by Yuriy Povstenko and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-03 with Mathematics categories.
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.
Linear Fractional Diffusion Wave Equation For Scientists And Engineers
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Author : Yuriy Povstenko
language : en
Publisher:
Release Date : 2015
Linear Fractional Diffusion Wave Equation For Scientists And Engineers written by Yuriy Povstenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the "long-tail" power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier's, Fick's and Darcy's laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.
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 Differential Equations
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Author : Zhi-Zhong Sun
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-24
Fractional Differential Equations written by Zhi-Zhong Sun 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 2020-08-24 with Mathematics categories.
Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
Fractional Partial Differential Equations And Their Numerical Solutions
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Author : Boling Guo
language : en
Publisher: World Scientific
Release Date : 2015-03-09
Fractional Partial Differential Equations And Their Numerical Solutions written by Boling Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-09 with Mathematics categories.
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.