Details

Subject(s)

• Fractional differential equations [Browse]

Series

• Applied Mathematical Sciences [More in this series]
• Applied Mathematical Sciences ; v.206 [More in this series]

Bibliographic references

Includes bibliographical references and index.

Source of description

Description based on print version record.

Contents

• Intro
• Preface
• Contents
• Acronyms
• Part I Preliminaries
• 1 Continuous Time Random Walk
• 1.1 Random Walk on a Lattice
• 1.2 Continuous Time Random Walk
• 1.3 Simulating Continuous Time Random Walk
• 2 Fractional Calculus
• 2.1 Gamma Function
• 2.2 Riemann-Liouville Fractional Integral
• 2.3 Fractional Derivatives
• 2.3.1 Riemann-Liouville fractional derivative
• 2.3.2 Djrbashian-Caputo fractional derivative
• 2.3.3 Grünwald-Letnikov fractional derivative
• 3 Mittag-Leffler and Wright Functions
• 3.1 Mittag-Leffler Function
• 3.1.1 Basic analytic properties
• 3.1.2 Mittag-Leffler function Eα,1(-x)
• 3.2 Wright Function
• 3.2.1 Basic analytic properties
• 3.2.2 Wright function Wρ,µ(-x)
• 3.3 Numerical Algorithms
• 3.3.1 Mittag-Leffler function Eα,β(z)
• 3.3.2 Wright function Wρ,µ(x)
• Part II Fractional Ordinary Differential Equations
• 4 Cauchy Problem for Fractional ODEs
• 4.1 Gronwall's Inequalities
• 4.2 ODEs with a Riemann-Liouville Fractional Derivative
• 4.3 ODEs with a Djrbashian-Caputo Fractional Derivative
• 5 Boundary Value Problem for Fractional ODEs
• 5.1 Green's Function
• 5.1.1 Riemann-Liouville case
• 5.1.2 Djrbashian-Caputo case
• 5.2 Variational Formulation
• 5.2.1 One-sided fractional derivatives
• 5.2.2 Two-sided mixed fractional derivatives
• 5.3 Fractional Sturm-Liouville Problem
• 5.3.1 Riemann-Liouville case
• 5.3.2 Djrbashian-Caputo case
• Part III Time-Fractional Diffusion
• 6 Subdiffusion: Hilbert Space Theory
• 6.1 Existence and Uniqueness in an Abstract Hilbert Space
• 6.2 Linear Problems with Time-Independent Coefficients
• 6.2.1 Solution representation
• 6.2.2 Existence, uniqueness and regularity
• 6.3 Linear Problems with Time-Dependent Coefficients
• 6.4 Nonlinear Subdiffusion
• 6.4.1 Lipschitz nonlinearity
• 6.4.2 Allen-Cahn equation.
• 6.4.3 Compressible Navier-Stokes problem
• 6.5 Maximum Principles
• 6.6 Inverse Problems
• 6.6.1 Backward subdiffusion
• 6.6.2 Inverse source problems
• 6.6.3 Determining fractional order
• 6.6.4 Inverse potential problem
• 6.7 Numerical Methods
• 6.7.1 Convolution quadrature
• 6.7.2 Piecewise polynomial interpolation
• 7 Subdiffusion: Hölder Space Theory
• 7.1 Fundamental Solutions
• 7.1.1 Fundamental solutions
• 7.1.2 Fractional θ-functions
• 7.2 Hölder Regularity in One Dimension
• 7.2.1 Subdiffusion in mathbbR
• 7.2.2 Subdiffusion in mathbbR+
• 7.2.3 Subdiffusion on bounded intervals
• 7.3 Hölder Regularity in Multi-Dimension
• 7.3.1 Subdiffusion in mathbbRd
• 7.3.2 Subdiffusion in mathbbRd+
• 7.3.3 Subdiffusion on bounded domains
• A Mathematical Preliminaries
• A.1 AC Spaces and Hölder Spaces
• A.1.1 AC spaces
• A.1.2 Hölder spaces
• A.2 Sobolev Spaces
• A.2.1 Lebesgue spaces
• A.2.2 Sobolev spaces
• A.2.3 Fractional Sobolev spaces
• A.2.4 s(Ω) spaces
• A.2.5 Bochner spaces
• A.3 Integral Transforms
• A.3.1 Laplace transform
• A.3.2 Fourier transform
• A.4 Fixed Point Theorems
• References
• Index.

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ISBN

3-030-76043-X

OCLC

1261380047

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