000			05418nam a2200313 i 4500
008			100415s2010 enka b 001 0 eng
020			_a9781848163294 _q(hardback)
020			_a1848163290 _q(hardback)
040			_aUKM _beng _cUKM _dBWK _dYDXCP _dBTCTA _dC#P _dBWX _dUtOrBLW _dBAUN _erda
049			_aBAUN_MERKEZ
050	0	4	_aQA314 _b.M35 2010
082	0	4	_222
100	1		_aMainardi, F. _q(Francesco), _d1942-
245	1	0	_aFractional calculus and waves in linear viscoelasticity : _ban introduction to mathematical models / _cFrancesco Mainardi
264		1	_aLondon ; _aHackensack, NJ : _bImperial College Press, _c[2010]
264		4	_c©2010
300			_axx, 347 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
504			_aIncludes bibliographical references and index
505	0	0	_tContents _t Preface _t Acknowledgements _t List of Figures _t1 Essentials of Fractional Calculus _t1.1 The fractional integral with support in IR+ _t1.2 The fractional derivative with support in IR+ _t1.3 Fractional relaxation equations in IR+ _t1.4 Fractional integrals and derivatives with support in IR _t1.5 Notes _t2 Essentials of Linear Viscoelasticity _t2.1 Introduction _t2.2 History in IR+: the Laplace transform approach _t2.3 The four types of viscoelasticity _t2.4 The classical mechanical models _t2.5 The time - and frequency - spectral functions _t2.6 History in IR: the Fourier transform approach and the dynamic functions _t2.7 Storage and dissipation of energy: the loss tangent _t2.8 The dynamic functions for the mechanical models _t2.9 Notes _t3 Fractional Viscoelastic Models _t3.1 The fractional calculus in the mechanical models _t3.1.1 Power-Law creep and the Scott-Blair model _t3.1.2 The correspondence principle _t3.1.3 The fractional mechanical models _t3.2 Analysis of the fractional Zener model _t3.2.1 The material and the spectral functions _t3.2.2 Dissipation: theoretical considerations _t3.2.3 Dissipation: experimental checks _t3.3 The physical interpretation of the fractional Zener model via fractional diffusion _t3.4 Which type of fractional derivative? Caputo or Riemann-Liouville? _t3.5 Notes _t4 Waves in Linear Viscoelastic Media: Dispersion and Dissipation _t4.1 Introduction _t4.2 Impact waves in linear viscoelasticity _t4.2.1 Statement of the problem by Laplace transforms _t4.2.2 The structure of wave equations in the space-time domain _t4.2.3 Evolution equations for the mechanical models _t4.3 Dispersion relation and complex refraction index _t4.3.1 Generalities _t4.3.2 Dispersion: phase velocity and group velocity _t4.3.3 Dissipation: the attenuation coefficient and the specific dissipation function _t4.3.4 Dispersion and attenuation for the Zener and the Maxwell models _t4.3.5 Dispersion and attenuation for the fractional Zener model _t4.3.6 The Klein-Gordon equation with dissipation _t4.4 The Brillouin signal velocity _t4.4.1 Generalities _t4.4.2 Signal velocity via steepest-descent path _t4.5 Notes _t5 Waves in Linear Viscoelastic Media: Asymptotic Representations _t5.1 The regular wave-front expansion _t5.2 The singular wave-front expansion _t5.3 The saddle-point approximation _t5.3.1 Generalities _t5.3.2 The Lee-Kanter problem for the Maxwell model _t5.3.3 The Jeffreys problem for the Zener model _t5.4 The matching between the wave-front and the saddle-point approximations _t6 Diffusion and Wave-Propagation via Fractional Calculus _t6.1 Introduction _t6.2 Derivation of the fundamental solutions _t6.3 Basic properties and plots of the Green functions _t6.4 The Signalling problem in a viscoelastic solid with a power-law creep _t6.5 Notes _tAppendix A The Eulerian Functions _tA.1 The Gamma function: Γ(z) _tA.2 The Beta function: B(p, q) _tA.3 Logarithmic derivative of the Gamma function _tA.4 The incomplete Gamma functions _tAppendix B The Bessel Functions _tB.1 The standard Bessel functions _tB.2 The modified Bessel functions _tB.3 Integral representations and Laplace transforms _tB.4 The Airy functions _tAppendix C The Error Functions _tC.1 The two standard Error functions _tC.2 Laplace transform pairs _tC.3 Repeated integrals of the Error functions _tC.4 The Erfi function and the Dawson integral _tC.5 The Fresnel integrals _tAppendix D The Exponential Integral Functions _tD.1 The classical Exponential integrals Ei(z), ε1(z) _tD.2 The modified Exponential integral Ein (z) _tD.3 Asymptotics for the Exponential integrals _tD.4 Laplace transform pairs for Exponential integrals _tAppendix E The Mittag-Leffler Functions _tE.1 The classical Mittag-Leffler function Ea(z) _tE.2 The Mittag-Leffler function with two parameters _tE.3 Other functions of the Mittag-Leffler type _tE.4 The Laplace transform pairs _tE.5 Derivatives of the Mittag-Leffler functions _tE.6 Summation and integration of Mittag-Leffler functions _tE.7 Applications of the Mittag-Leffler functions to the Abel integral equations _tE.8 Notes _tAppendix F The Wright Functions _tF.1 The Wright function Wλ,μ(z) _tF.2 The auxiliary functions Fv(z) and Mv(z) in C _tF.3 The auxiliary functions Fv(x) and Mv(x) in IR _tF.4 The Laplace transform pairs _tF.5 The Wright M-functions in probability _tF.6 Notes _t Bibliography _t Index
650		0	_aFractional calculus
650		0	_aWaves _xMathematical models
650		0	_aViscoelasticity _xMathematical models
710	2		_928005 _aImperial College Press.
900			_a31266
942			_2lcc _cKT
999			_c27799 _d27799