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Fractional calculus with applications in mechanics : vibrations and diffusion processes / Teodor M. Atanacković...[ET AL.]
| Fractional calculus with applications in mechanics : vibrations and diffusion processes / Teodor M. Atanacković...[ET AL.] |
| Pubbl/distr/stampa | London ; Hoboken, : ISTE, : Wiley, 2014 |
| Descrizione fisica | Testo elettronico (PDF) (XIII, 315 p.) |
| Disciplina | 531.0151583 |
| Collana | Mechanical engineering and solid mechanics series. |
| Soggetto topico | Calcolo frazionario |
| ISBN | 9781118577530 |
| Formato | Risorse elettroniche  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996451649403316 |
| London ; Hoboken, : ISTE, : Wiley, 2014 | ||
| Risorse elettroniche | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fractional calculus with applications in mechanics : vibrations and diffusion processes / / Teodor M. Atanacković [and three others]
| Fractional calculus with applications in mechanics : vibrations and diffusion processes / / Teodor M. Atanacković [and three others] |
| Pubbl/distr/stampa | London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina | 531.0151583 |
| Collana | Mechanical Engineering and Solid Mechanics Series |
| Soggetto topico |
Fractional calculus
Mechanics - Mathematics |
| ISBN |
1-118-57753-1
1-118-57750-7 1-118-57746-9 |
| 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
2.1.2. Riemann-Liouville fractional integrals and derivatives on the real half-axis2.1.3. 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; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative; 2.2.2. Taylor theorem for fractional derivatives; 2.3. 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 derivativePART 2. MECHANICAL SYSTEMS; Chapter 3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body; 3.1. Method based on the Fourier transform; 3.1.1. Linear fractional model; 3.1.2. Distributed-order fractional model; 3.1.3. Constitutive equations for rod bending; 3.1.4. Stress relaxation and creep for two special cases of viscoelastic bodies; 3.1.5. Variable-order fractional derivative: application to stress relaxation problem 3.1.6. Linear constitutive equation with fractional derivatives of complex order3.2. Thermodynamical restrictions via the internal variable theory; 3.2.1. Case I; 3.2.2. Case II; Chapter 4. Vibrations with Fractional Dissipation; 4.1. Linear vibrations with fractional dissipation; 4.1.1. Linear vibrations with the single fractional dissipation term; 4.1.2. Fractional derivative-type creeping motion; 4.1.3. Linear vibrations with the multiterm fractional dissipation; 4.1.4. Linear fractional two-compartmental model with fractional derivatives of different order; 4.2. Bagley-Torvik equation 4.2.1. Solution procedure4.2.2. Numerical examples; 4.3. Nonlinear vibrations with symmetrized fractional dissipation; 4.3.1. Solvability and dissipativity of [4.58]; 4.3.2. Stability of the solution; 4.4. Nonlinear vibrations with distributed-order fractional dissipation; 4.4.1. Existence of solutions; 4.4.2. Uniqueness of solutions; 4.4.3. Nonlinear vibrations with single term of fractional dissipation; Chapter 5. Lateral Vibrations and Stability of Viscoelastic Rods; 5.1. Lateral vibrations and creep of a fractional type viscoelastic rod 5.1.1. Rod made of fractional Kelvin-Voigt-type material |
| Record Nr. | UNINA-9910140289003321 |
| London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus with applications in mechanics : vibrations and diffusion processes / / Teodor M. Atanacković [and three others]
| Fractional calculus with applications in mechanics : vibrations and diffusion processes / / Teodor M. Atanacković [and three others] |
| Pubbl/distr/stampa | London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (331 p.) |
| Disciplina | 531.0151583 |
| Collana | Mechanical Engineering and Solid Mechanics Series |
| Soggetto topico |
Fractional calculus
Mechanics - Mathematics |
| ISBN |
1-118-57753-1
1-118-57750-7 1-118-57746-9 |
| 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
2.1.2. Riemann-Liouville fractional integrals and derivatives on the real half-axis2.1.3. 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; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative; 2.2.2. Taylor theorem for fractional derivatives; 2.3. 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 derivativePART 2. MECHANICAL SYSTEMS; Chapter 3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body; 3.1. Method based on the Fourier transform; 3.1.1. Linear fractional model; 3.1.2. Distributed-order fractional model; 3.1.3. Constitutive equations for rod bending; 3.1.4. Stress relaxation and creep for two special cases of viscoelastic bodies; 3.1.5. Variable-order fractional derivative: application to stress relaxation problem 3.1.6. Linear constitutive equation with fractional derivatives of complex order3.2. Thermodynamical restrictions via the internal variable theory; 3.2.1. Case I; 3.2.2. Case II; Chapter 4. Vibrations with Fractional Dissipation; 4.1. Linear vibrations with fractional dissipation; 4.1.1. Linear vibrations with the single fractional dissipation term; 4.1.2. Fractional derivative-type creeping motion; 4.1.3. Linear vibrations with the multiterm fractional dissipation; 4.1.4. Linear fractional two-compartmental model with fractional derivatives of different order; 4.2. Bagley-Torvik equation 4.2.1. Solution procedure4.2.2. Numerical examples; 4.3. Nonlinear vibrations with symmetrized fractional dissipation; 4.3.1. Solvability and dissipativity of [4.58]; 4.3.2. Stability of the solution; 4.4. Nonlinear vibrations with distributed-order fractional dissipation; 4.4.1. Existence of solutions; 4.4.2. Uniqueness of solutions; 4.4.3. Nonlinear vibrations with single term of fractional dissipation; Chapter 5. Lateral Vibrations and Stability of Viscoelastic Rods; 5.1. Lateral vibrations and creep of a fractional type viscoelastic rod 5.1.1. Rod made of fractional Kelvin-Voigt-type material |
| Record Nr. | UNINA-9910815422803321 |
| London ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||