05449nam 2200685 450 991081542280332120200520144314.01-118-57753-11-118-57750-71-118-57746-9(CKB)2670000000530779(EBL)1637656(SSID)ssj0001211953(PQKBManifestationID)11770305(PQKBTitleCode)TC0001211953(PQKBWorkID)11206128(PQKB)10388969(OCoLC)878138765(MiAaPQ)EBC1637656(Au-PeEL)EBL1637656(CaPaEBR)ebr10843881(CaONFJC)MIL578537(OCoLC)871224309(PPN)184538254(EXLCZ)99267000000053077920140324h20142014 uy 0engur|n|---|||||txtccrFractional calculus with applications in mechanics vibrations and diffusion processes /Teodor M. Atanacković [and three others]London ;Hoboken, New Jersey :ISTE :Wiley,2014.©20141 online resource (331 p.)Mechanical Engineering and Solid Mechanics SeriesDescription based upon print version of record.1-84821-417-0 Includes bibliographical references and index.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 derivatives2.1.2. 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 order2.3.3. 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 problem3.1.6. 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 equation4.2.1. 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 rod5.1.1. Rod made of fractional Kelvin-Voigt-type material This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton-type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed nMechanical engineering and solid mechanics series.Fractional calculusMechanicsMathematicsFractional calculus.MechanicsMathematics.531.0151583Atanacković Teodor M.MiAaPQMiAaPQMiAaPQBOOK9910815422803321Fractional calculus with applications in mechanics2260698UNINA