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Fractional calculus and waves in linear viscoelasticity [[electronic resource] ] : an introduction to mathematical models / / Francesco Mainardi
| Fractional calculus and waves in linear viscoelasticity [[electronic resource] ] : an introduction to mathematical models / / Francesco Mainardi |
| Autore | Mainardi F (Francesco), <1942-> |
| Pubbl/distr/stampa | London, : Imperial College Press, c2010 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina | 531.1133 |
| Soggetto topico |
Fractional calculus
Waves - Mathematical models Viscoelasticity - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75983-3
9786612759833 1-84816-330-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Acknowledgements; Contents; List of Figures; 1. Essentials of Fractional Calculus; 2. Essentials of Linear Viscoelasticity; 3. Fractional Viscoelastic Models; 4. Waves in Linear Viscoelastic Media: Dispersion and Dissipation; 5. Waves in Linear Viscoelastic Media: Asymptotic Representations; 6. Diffusion and Wave-Propagation via Fractional Calculus; Appendix A The Eulerian Functions; Appendix B The Bessel Functions; Appendix C The Error Functions; Appendix D The Exponential Integral Functions; Appendix E The Mittag-Leffler Functions; Appendix F The Wright Functions; Bibliography
Index |
| Record Nr. | UNINA-9910456184103321 |
Mainardi F (Francesco), <1942->
|
||
| London, : Imperial College Press, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus and waves in linear viscoelasticity [[electronic resource] ] : an introduction to mathematical models / / Francesco Mainardi
| Fractional calculus and waves in linear viscoelasticity [[electronic resource] ] : an introduction to mathematical models / / Francesco Mainardi |
| Autore | Mainardi F (Francesco), <1942-> |
| Pubbl/distr/stampa | London, : Imperial College Press, c2010 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina | 531.1133 |
| Soggetto topico |
Fractional calculus
Waves - Mathematical models Viscoelasticity - Mathematical models |
| ISBN |
1-282-75983-3
9786612759833 1-84816-330-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Acknowledgements; Contents; List of Figures; 1. Essentials of Fractional Calculus; 2. Essentials of Linear Viscoelasticity; 3. Fractional Viscoelastic Models; 4. Waves in Linear Viscoelastic Media: Dispersion and Dissipation; 5. Waves in Linear Viscoelastic Media: Asymptotic Representations; 6. Diffusion and Wave-Propagation via Fractional Calculus; Appendix A The Eulerian Functions; Appendix B The Bessel Functions; Appendix C The Error Functions; Appendix D The Exponential Integral Functions; Appendix E The Mittag-Leffler Functions; Appendix F The Wright Functions; Bibliography
Index |
| Record Nr. | UNINA-9910780877503321 |
|
Mainardi F (Francesco), <1942->
|
||
| London, : Imperial College Press, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models / / Francesco Mainardi
| Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models / / Francesco Mainardi |
| Autore | Mainardi F (Francesco), <1942-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | London, : Imperial College Press, c2010 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina | 531.1133 |
| Soggetto topico |
Fractional calculus
Waves - Mathematical models Viscoelasticity - Mathematical models |
| ISBN |
1-282-75983-3
9786612759833 1-84816-330-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Acknowledgements; Contents; List of Figures; 1. Essentials of Fractional Calculus; 2. Essentials of Linear Viscoelasticity; 3. Fractional Viscoelastic Models; 4. Waves in Linear Viscoelastic Media: Dispersion and Dissipation; 5. Waves in Linear Viscoelastic Media: Asymptotic Representations; 6. Diffusion and Wave-Propagation via Fractional Calculus; Appendix A The Eulerian Functions; Appendix B The Bessel Functions; Appendix C The Error Functions; Appendix D The Exponential Integral Functions; Appendix E The Mittag-Leffler Functions; Appendix F The Wright Functions; Bibliography
Index |
| Record Nr. | UNINA-9910821263103321 |
|
Mainardi F (Francesco), <1942->
|
||
| London, : Imperial College Press, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models / Francesco Mainardi
| Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models / Francesco Mainardi |
| Autore | Mainardi, Francesco |
| Pubbl/distr/stampa | London : Imperial College Press, c2010 |
| Descrizione fisica | xx, 347 p. : ill. ; 24 cm |
| Disciplina | 531.1133 |
| Soggetto topico |
Fractional calculus
Waves - Mathematical models Viscoelasticity - Mathematical models |
| ISBN | 9781848163294 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003580679707536 |
|
Mainardi, Francesco
|
||
| London : Imperial College Press, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel
| Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel |
| Pubbl/distr/stampa | London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (424 p.) |
| Disciplina | 515 |
| Altri autori (Persone) |
AtanackovićTeodor M
ChallamelNoël |
| Collana | Mechanical Engineering and Solid Mechanics Series |
| Soggetto topico |
Calculus
Fractional calculus Viscoelasticity - Mathematical models Waves - Mathematical models |
| ISBN |
1-118-90913-5
1-118-90906-2 1-118-90901-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Contents; Preface; PART 1. MATHEMATICAL PRELIMINARIES, DEFINITIONS AND PROPERTIES OF FRACTIONAL INTEGRALS AND DERIVATIVES; Chapter 1. Mathematical Preliminaries; 1.1. Notation and definitions; 1.2. Laplace transform of a function; 1.3. Spaces of distributions; 1.4. Fundamental solution; 1.5. Some special functions; Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives; 2.1. Definitions of fractional integrals and derivatives; 2.1.1. Riemann-Liouville fractional integrals and derivatives
2.1.1.1. Laplace transform of Riemann-Liouville fractional integrals and derivatives2.1.2. Riemann-Liouville fractional integrals and derivatives on the real half-axis; 2.1.3. Caputo fractional derivatives; 2.1.4. Riesz potentials and Riesz derivatives; 2.1.5. Symmetrized Caputo derivative; 2.1.6. Other types of fractional derivatives; 2.1.6.1. Canavati fractional derivative; 2.1.6.2. Marchaud fractional derivatives; 2.1.6.3. Grünwald-Letnikov fractional derivatives; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative 2.2.2. Taylor theorem for fractional derivatives2.3. Fractional derivatives in distributional setting; 2.3.1. Definition of the fractional integral and derivative; 2.3.2. Dependence of fractional derivative on order; 2.3.3. Distributed-order fractional derivative; PART 2. MECHANICAL SYSTEMS; Chapter 3. Waves in Viscoelastic Materials of Fractional-Order Type; 3.1. Time-fractional wave equation on unbounded domain; 3.1.1. Time-fractional Zener wave equation; 3.1.2. Time-fractional general linear wave equation; 3.1.3. Numerical examples; 3.1.3.1. Case of time-fractional Zener wave equation 3.1.3.2. Case of time-fractional general linear wave equation3.2. Wave equation of the fractional Eringen-type; 3.3. Space-fractional wave equation on unbounded domain; 3.3.1. Solution to Cauchy problem for space-fractional wave equation; 3.3.1.1. Limiting case ß -> 1; 3.3.1.2. Case u0(x)...; 3.3.1.3. Case u0 (x)...; 3.3.1.4. Case u0(x)...; 3.3.2. Solution to Cauchy problem for fractionally damped space-fractional wave equation; 3.4. Stress relaxation, creep and forced oscillations of a viscoelastic rod; 3.4.1. Formal solution to systems [3.110]-[3.112], [3.113] and either [3.114] or [3.115] 3.4.1.1. Displacement of rod's end Υ is prescribed by [3.120]3.4.1.2. Stress at rod's end Σ is prescribed by [3.121]; 3.4.2. Case of solid-like viscoelastic body; 3.4.2.1. Determination of the displacement u in a stress relaxation test; 3.4.2.2. Case Υ = Υ0H + F; 3.4.2.3. Determination of the stress s in a stress relaxation test; 3.4.2.4. Determination of displacement u in the case of prescribed stress; 3.4.2.5. Numerical examples; 3.4.3. Case of fluid-like viscoelastic body; 3.4.3.1. Determination of the displacement u in a stress relaxation test 3.4.3.2. Determination of the stress σ in a stress relaxation test |
| Record Nr. | UNISA-996211734903316 |
| London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel
| Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel |
| Pubbl/distr/stampa | London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (424 p.) |
| Disciplina | 515 |
| Altri autori (Persone) |
AtanackovićTeodor M
ChallamelNoël |
| Collana | Mechanical Engineering and Solid Mechanics Series |
| Soggetto topico |
Calculus
Fractional calculus Viscoelasticity - Mathematical models Waves - Mathematical models |
| ISBN |
1-118-90913-5
1-118-90906-2 1-118-90901-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Contents; Preface; PART 1. MATHEMATICAL PRELIMINARIES, DEFINITIONS AND PROPERTIES OF FRACTIONAL INTEGRALS AND DERIVATIVES; Chapter 1. Mathematical Preliminaries; 1.1. Notation and definitions; 1.2. Laplace transform of a function; 1.3. Spaces of distributions; 1.4. Fundamental solution; 1.5. Some special functions; Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives; 2.1. Definitions of fractional integrals and derivatives; 2.1.1. Riemann-Liouville fractional integrals and derivatives
2.1.1.1. Laplace transform of Riemann-Liouville fractional integrals and derivatives2.1.2. Riemann-Liouville fractional integrals and derivatives on the real half-axis; 2.1.3. Caputo fractional derivatives; 2.1.4. Riesz potentials and Riesz derivatives; 2.1.5. Symmetrized Caputo derivative; 2.1.6. Other types of fractional derivatives; 2.1.6.1. Canavati fractional derivative; 2.1.6.2. Marchaud fractional derivatives; 2.1.6.3. Grünwald-Letnikov fractional derivatives; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative 2.2.2. Taylor theorem for fractional derivatives2.3. Fractional derivatives in distributional setting; 2.3.1. Definition of the fractional integral and derivative; 2.3.2. Dependence of fractional derivative on order; 2.3.3. Distributed-order fractional derivative; PART 2. MECHANICAL SYSTEMS; Chapter 3. Waves in Viscoelastic Materials of Fractional-Order Type; 3.1. Time-fractional wave equation on unbounded domain; 3.1.1. Time-fractional Zener wave equation; 3.1.2. Time-fractional general linear wave equation; 3.1.3. Numerical examples; 3.1.3.1. Case of time-fractional Zener wave equation 3.1.3.2. Case of time-fractional general linear wave equation3.2. Wave equation of the fractional Eringen-type; 3.3. Space-fractional wave equation on unbounded domain; 3.3.1. Solution to Cauchy problem for space-fractional wave equation; 3.3.1.1. Limiting case ß -> 1; 3.3.1.2. Case u0(x)...; 3.3.1.3. Case u0 (x)...; 3.3.1.4. Case u0(x)...; 3.3.2. Solution to Cauchy problem for fractionally damped space-fractional wave equation; 3.4. Stress relaxation, creep and forced oscillations of a viscoelastic rod; 3.4.1. Formal solution to systems [3.110]-[3.112], [3.113] and either [3.114] or [3.115] 3.4.1.1. Displacement of rod's end Υ is prescribed by [3.120]3.4.1.2. Stress at rod's end Σ is prescribed by [3.121]; 3.4.2. Case of solid-like viscoelastic body; 3.4.2.1. Determination of the displacement u in a stress relaxation test; 3.4.2.2. Case Υ = Υ0H + F; 3.4.2.3. Determination of the stress s in a stress relaxation test; 3.4.2.4. Determination of displacement u in the case of prescribed stress; 3.4.2.5. Numerical examples; 3.4.3. Case of fluid-like viscoelastic body; 3.4.3.1. Determination of the displacement u in a stress relaxation test 3.4.3.2. Determination of the stress σ in a stress relaxation test |
| Record Nr. | UNINA-9910140286903321 |
| London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel
| Fractional calculus with applications in mechanics : wave propagation, impact and variational principles / / Teodor M. Atanacković [and three others] ; series editor, Noël Challamel |
| Pubbl/distr/stampa | London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (424 p.) |
| Disciplina | 515 |
| Altri autori (Persone) |
AtanackovićTeodor M
ChallamelNoël |
| Collana | Mechanical Engineering and Solid Mechanics Series |
| Soggetto topico |
Calculus
Fractional calculus Viscoelasticity - Mathematical models Waves - Mathematical models |
| ISBN |
1-118-90913-5
1-118-90906-2 1-118-90901-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Contents; Preface; PART 1. MATHEMATICAL PRELIMINARIES, DEFINITIONS AND PROPERTIES OF FRACTIONAL INTEGRALS AND DERIVATIVES; Chapter 1. Mathematical Preliminaries; 1.1. Notation and definitions; 1.2. Laplace transform of a function; 1.3. Spaces of distributions; 1.4. Fundamental solution; 1.5. Some special functions; Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives; 2.1. Definitions of fractional integrals and derivatives; 2.1.1. Riemann-Liouville fractional integrals and derivatives
2.1.1.1. Laplace transform of Riemann-Liouville fractional integrals and derivatives2.1.2. Riemann-Liouville fractional integrals and derivatives on the real half-axis; 2.1.3. Caputo fractional derivatives; 2.1.4. Riesz potentials and Riesz derivatives; 2.1.5. Symmetrized Caputo derivative; 2.1.6. Other types of fractional derivatives; 2.1.6.1. Canavati fractional derivative; 2.1.6.2. Marchaud fractional derivatives; 2.1.6.3. Grünwald-Letnikov fractional derivatives; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative 2.2.2. Taylor theorem for fractional derivatives2.3. Fractional derivatives in distributional setting; 2.3.1. Definition of the fractional integral and derivative; 2.3.2. Dependence of fractional derivative on order; 2.3.3. Distributed-order fractional derivative; PART 2. MECHANICAL SYSTEMS; Chapter 3. Waves in Viscoelastic Materials of Fractional-Order Type; 3.1. Time-fractional wave equation on unbounded domain; 3.1.1. Time-fractional Zener wave equation; 3.1.2. Time-fractional general linear wave equation; 3.1.3. Numerical examples; 3.1.3.1. Case of time-fractional Zener wave equation 3.1.3.2. Case of time-fractional general linear wave equation3.2. Wave equation of the fractional Eringen-type; 3.3. Space-fractional wave equation on unbounded domain; 3.3.1. Solution to Cauchy problem for space-fractional wave equation; 3.3.1.1. Limiting case ß -> 1; 3.3.1.2. Case u0(x)...; 3.3.1.3. Case u0 (x)...; 3.3.1.4. Case u0(x)...; 3.3.2. Solution to Cauchy problem for fractionally damped space-fractional wave equation; 3.4. Stress relaxation, creep and forced oscillations of a viscoelastic rod; 3.4.1. Formal solution to systems [3.110]-[3.112], [3.113] and either [3.114] or [3.115] 3.4.1.1. Displacement of rod's end Υ is prescribed by [3.120]3.4.1.2. Stress at rod's end Σ is prescribed by [3.121]; 3.4.2. Case of solid-like viscoelastic body; 3.4.2.1. Determination of the displacement u in a stress relaxation test; 3.4.2.2. Case Υ = Υ0H + F; 3.4.2.3. Determination of the stress s in a stress relaxation test; 3.4.2.4. Determination of displacement u in the case of prescribed stress; 3.4.2.5. Numerical examples; 3.4.3. Case of fluid-like viscoelastic body; 3.4.3.1. Determination of the displacement u in a stress relaxation test 3.4.3.2. Determination of the stress σ in a stress relaxation test |
| Record Nr. | UNINA-9910807155803321 |
| London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri
| Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri |
| Autore | Ionescu Alexandru D. |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (v, 123 pages) |
| Disciplina | 531.1133015118 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Waves - Mathematical models
Water waves - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4917-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910480226703321 |
|
Ionescu Alexandru D.
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri
| Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri |
| Autore | Ionescu Alexandru D. |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (v, 123 pages) |
| Disciplina | 531.1133015118 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Waves - Mathematical models
Water waves - Mathematical models |
| ISBN | 1-4704-4917-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910793321603321 |
|
Ionescu Alexandru D.
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri
| Global regularity for 2D water waves with surface tension / / Alexandru D. Ionescu, Fabio Pusateri |
| Autore | Ionescu Alexandru D. |
| Pubbl/distr/stampa | Providence, RI : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (v, 123 pages) |
| Disciplina | 531.1133015118 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Waves - Mathematical models
Water waves - Mathematical models |
| ISBN | 1-4704-4917-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910817565803321 |
|
Ionescu Alexandru D.
|
||
| Providence, RI : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
