LEADER 05786nam 2200733 450 001 996211734903316 005 20230803195408.0 010 $a1-118-90913-5 010 $a1-118-90906-2 010 $a1-118-90901-1 035 $a(CKB)2670000000530806 035 $a(EBL)1638168 035 $a(SSID)ssj0001158640 035 $a(PQKBManifestationID)11622936 035 $a(PQKBTitleCode)TC0001158640 035 $a(PQKBWorkID)11107046 035 $a(PQKB)10849633 035 $a(OCoLC)876043683 035 $a(MiAaPQ)EBC1638168 035 $a(Au-PeEL)EBL1638168 035 $a(CaPaEBR)ebr10842298 035 $a(CaONFJC)MIL578584 035 $a(OCoLC)871224267 035 $a(EXLCZ)992670000000530806 100 $a20140313h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aFractional calculus with applications in mechanics $ewave propagation, impact and variational principles /$fTeodor M. Atanackovic? [and three others] ; series editor, Noe?l Challamel 210 1$aLondon ;$aHoboken, New Jersey :$cISTE :$cWiley,$d2014. 210 4$d©2014 215 $a1 online resource (424 p.) 225 1 $aMechanical Engineering and Solid Mechanics Series 300 $aDescription based upon print version of record. 311 $a1-84821-679-3 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $a2.1.1.1. 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. Gru?nwald-Letnikov fractional derivatives; 2.2. Some additional properties of fractional derivatives; 2.2.1. Fermat theorem for fractional derivative 327 $a2.2.2. 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 327 $a3.1.3.2. 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] 327 $a3.4.1.1. Displacement of rod's end ? is prescribed by [3.120]3.4.1.2. Stress at rod's end ? 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 ? = ?0H + 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 327 $a3.4.3.2. Determination of the stress ? in a stress relaxation test 330 $a The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscilla 410 0$aFocus series in mechanical engineering and solid mechanics. 606 $aCalculus 606 $aFractional calculus 606 $aViscoelasticity$xMathematical models 606 $aWaves$xMathematical models 615 0$aCalculus. 615 0$aFractional calculus. 615 0$aViscoelasticity$xMathematical models. 615 0$aWaves$xMathematical models. 676 $a515 701 $aAtanackovic?$b Teodor M$0499507 701 $aChallamel$b Noe?l$0974470 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996211734903316 996 $aFractional calculus with applications in mechanics$92292237 997 $aUNISA