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Fractional differential equations : an approach via fractional derivatives / / Bangti Jin
| Fractional differential equations : an approach via fractional derivatives / / Bangti Jin |
| Autore | Jin Bangti |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (377 pages) |
| Disciplina | 515.35 |
| Collana | Applied Mathematical Sciences |
| Soggetto topico |
Fractional differential equations
Equacions diferencials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-76043-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 -- References -- Index. |
| Record Nr. | UNISA-996466415303316 |
Jin Bangti
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fractional differential equations : an approach via fractional derivatives / / Bangti Jin
| Fractional differential equations : an approach via fractional derivatives / / Bangti Jin |
| Autore | Jin Bangti |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (377 pages) |
| Disciplina | 515.35 |
| Collana | Applied Mathematical Sciences |
| Soggetto topico |
Fractional differential equations
Equacions diferencials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-76043-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 -- References -- Index. |
| Record Nr. | UNINA-9910495197503321 |
|
Jin Bangti
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical treatment and analysis of time-fractional evolution equations / / Bangti Jin, Zhi Zhou
| Numerical treatment and analysis of time-fractional evolution equations / / Bangti Jin, Zhi Zhou |
| Autore | Jin Bangti |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
| Descrizione fisica | 1 online resource (428 pages) |
| Disciplina | 929.374 |
| Collana | Applied Mathematical Sciences |
| Soggetto topico | Evolution equations |
| ISBN | 3-031-21050-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Existence, Uniqueness, and Regularity of Solutions -- Semidiscrete Discretization -- Convolution Quadrature -- Finite Difference Methods: Construction and Implementation -- Finite Difference Methods on Uniform Meshes -- Finite Difference Methods on Graded Meshes -- Nonnegativity Preservation -- Discrete Fractional Maximal Regularity -- Subdiffusion with time-dependent coefficients -- Semilinear Subdiffusion Equations -- Time-Space Formulation and Finite Element Approximation -- A Spectral Petrov-Galerkin Method -- Incomplete Iterative Solution at the Time Levels -- Optimal Control with Subdiffusion Constraint -- Backward Subdiffusion Problems -- Appendix: Mathematical Preliminaries. |
| Record Nr. | UNINA-9910674345203321 |
|
Jin Bangti
|
||
| Cham, Switzerland : , : Springer, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||