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Atanacković, T. M., Pilipović, S., Stanković, B., and Zorica, D. S. (2014), Fractional calculus with applications in mechanics: Wave propagation, impact and variational principles, Mechanical Engineering and Solid Mechanics Series. ISTE, London; John Wiley & Sons, Inc., Hoboken, NJ., 10.1002/9781118909065AtanackovićT. M.PilipovićS.StankovićB.ZoricaD. S.2014Fractional calculus with applications in mechanics: Wave propagation, impact and variational principlesLondon; John Wiley & Sons, IncHoboken, NJ10.1002/9781118909065Open DOISearch in Google Scholar
Atanacković, T. M., Pilipović, S., Stanković, B., and Zorica, D. S. (2014), Fractional calculus with applications in mechanics: Vibrations and diffusion processes, Mechanical Engineering and Solid Mechanics Series. ISTE, London; John Wiley & Sons, Inc., Hoboken, NJ., 10.1002/9781118577530AtanackovićT. M.PilipovićS.StankovićB.ZoricaD. S.2014Fractional calculus with applications in mechanics: Vibrations and diffusion processesLondon; John Wiley & Sons, IncHoboken, NJ10.1002/9781118577530Open DOISearch in Google Scholar
Bamberger, A. and Duong, T. H. (1986), Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d’une onde acoustique. I, Math. Methods Appl. Sci. 8(1), pp. 405–435, 10.1002/mma.1670080127BambergerA.DuongT. H.1986Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction ďune onde acoustique8140543510.1002/mma.1670080127Open DOISearch in Google Scholar
Banjai, L. and Schanz, M. (2012), Wave propagation problems treated with convolution quadrature and BEM, Fast boundary element methods in engineering and industrial applications, pp. 145–184, Lect. Notes Appl. Comput. Mech., 63, Springer, Heidelberg, 10.1007/978-3-642-25670-7_5BanjaiL.SchanzM.2012Wave propagation problems treated with convolution quadrature and BEM, Fast boundary element methods in engineering and industrial applications14518463SpringerHeidelberg10.1007/978-3-642-25670-7_5Open DOISearch in Google Scholar
Bécache, E., Ezziani, A., and Joly, P. (2004), A mixed finite element approach for viscoelastic wave propagation, Comput. Geosci. 8(3), pp. 255–299, 10.1007/s10596-005-3772-8BécacheE.EzzianiA.JolyP.2004A mixed finite element approach for viscoelastic wave propagation8325529910.1007/s10596-005-3772-8Open DOISearch in Google Scholar
Colombaro, I., Giusti, A., and Mainardi, F. (2017), On the propagation of transient waves in a viscoelastic Bessel medium, Z. Angew. Math. Phys. 68(3), Art. 62, 13 pp., 10.1007/s00033-017-0808-6ColombaroI.GiustiA.MainardiF.2017On the propagation of transient waves in a viscoelastic Bessel medium683621310.1007/s00033-017-0808-6Open DOISearch in Google Scholar
Colombaro, I., Giusti, A., and Mainardi, F. (2017), On transient waves in linear viscoelasticity, Wave Motion74, pp. 191–212, 10.1016/j.wavemoti.2017.07.008ColombaroI.GiustiA.MainardiF.2017On transient waves in linear viscoelasticity7419121210.1016/j.wavemoti.2017.07.008Open DOISearch in Google Scholar
Fabrizio, M. and Morro, A. (1992), Mathematical problems in linear viscoelasticity, SIAM Studies in Applied Mathematics12, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 10.1137/1.9781611970807FabrizioM.MorroA.1992Mathematical problems in linear viscoelasticity12Society for Industrial and Applied Mathematics (SIAM)Philadelphia, PA10.1137/1.9781611970807Open DOISearch in Google Scholar
Giusti, A. and Colombaro, I. (2018), Prabhakar-like fractional viscoelasticity, Commun. Nonlinear Sci. Numer. Simul. 56, pp. 138–143, 10.1016/j.cnsns.2017.08.002GiustiA.ColombaroI.2018Prabhakar-like fractional viscoelasticity5613814310.1016/j.cnsns.2017.08.002Open DOISearch in Google Scholar
Gurtin, M. E. and Sternberg, E. (1962), On the linear theory of viscoelasticity, Arch. Rational Mech. Anal. 11, pp. 291–356, 10.1007/bf00253942GurtinM. E.SternbergE.1962On the linear theory of viscoelasticity1129135610.1007/bf00253942Open DOISearch in Google Scholar
Hassell, M. and Sayas, F.-J. (2016), Convolution quadrature for wave simulations, Numerical simulation in physics and engineering, pp. 71–159, SEMA SIMAI Springer Ser., 9, Springer, [Cham], 10.1007/978-3-319-32146-2_2HassellM.SayasF.J.2016Convolution quadrature for wave simulations71159SEMA SIMAI Springer Ser9SpringerCham10.1007/978-3-319-32146-2_2Open DOISearch in Google Scholar
Keramat, A. and Heidari Shirazi, K. (2014), Finite element based dynamic analysis of viscoelastic solids using the approximation of Volterra integrals, Finite Elem. Anal. Des. 86, pp. 89–100, 10.1016/j.finel.2014.03.010KeramatA.Heidari ShiraziK.2014Finite element based dynamic analysis of viscoelastic solids using the approximation of Volterra integrals868910010.1016/j.finel.2014.03.010Open DOISearch in Google Scholar
Larsson, S., Racheva, M., and Saedpanah, F. (2015), Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity, Comput. Methods Appl. Mech. Engrg. 283, pp. 196–209, 10.1016/j.cma.2014.09.018LarssonS.RachevaM.SaedpanahF.2015Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity28319620910.1016/j.cma.2014.09.018Open DOISearch in Google Scholar
Lee, J. J. (2017), Analysis of mixed finite element methods for the standard linear solid model in viscoelasticity, Calcolo54(2), pp. 587–607, 10.1007/s10092-016-0200-5LeeJ. J.2017Analysis of mixed finite element methods for the standard linear solid model in viscoelasticity54258760710.1007/s10092-016-0200-5Open DOISearch in Google Scholar
Li, H., Zhao, Z., and Luo, Z. (2016), A space-time continuous finite element method for 2D viscoelastic wave equation, Bound. Value Probl. Paper No. 53, 17 pp., 10.1186/s13661-016-0563-1LiH.ZhaoZ.LuoZ.2016A space-time continuous finite element method for 2D viscoelastic wave equation531710.1186/s13661-016-0563-1Open DOISearch in Google Scholar
Lu, J.-F. and Hanyga, A. (2004), Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory, Geophys. J. Int. 159(2), pp. 688–702, 10.1111/j.1365-246x.2004.02409.xLuJ.F.HanygaA.2004Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory159268870210.1111/j.1365-246x.2004.02409.xOpen DOISearch in Google Scholar
Lubich, C. (1994), On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer. Math. 67(3), pp. 365–389, 10.1007/s002110050033LubichC.1994On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations67336538910.1007/s002110050033Open DOISearch in Google Scholar
Mainardi, F. (1982), Wave propagation in viscoelastic media, Pitman Advanced Pub. ProgramMainardiF.1982Wave propagation in viscoelastic media10.1115/1.3167123Search in Google Scholar
Mainardi, F. (2010), Fractional calculus and waves in linear viscoelasticity: An introduction to mathematical models, Imperial College Press, London, 10.1142/9781848163300MainardiF.2010Fractional calculus and waves in linear viscoelasticity: An introduction to mathematical modelsLondon10.1142/9781848163300Open DOISearch in Google Scholar
Mainardi, F. (2012), An historical perspective on fractional calculus in linear viscoelasticity, Fract. Calc. Appl. Anal. 15(4), pp. 712–717, 10.2478/s13540-012-0048-6MainardiF.2012An historical perspective on fractional calculus in linear viscoelasticity15471271710.2478/s13540-012-0048-6Open DOISearch in Google Scholar
Mainardi, F. (2018), A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients, Mathematics6(1), 10.3390/math6010008MainardiF.2018A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients6110.3390/math6010008Open DOISearch in Google Scholar
Mainardi, F. and Gorenflo, R. (2000), On Mittag-Leffler-type functions in fractional evolution processes, J. Comput. Appl. Math. 118(1-2), pp. 283–299, 10.1016/s0377-0427(00)00294-6MainardiF.GorenfloR.2000On Mittag-Leffler-type functions in fractional evolution processes1181-228329910.1016/s0377-0427(00)00294-6Open DOISearch in Google Scholar
Marques, S. P. C. and Creus, G. J. (2012), Computational Viscoelasticity, Springer Berlin Heidelberg, 10.1007/978-3-642-25311-9MarquesS. P. C.CreusG. J.2012Springer Berlin Heidelberg10.1007/978-3-642-25311-9Open DOISearch in Google Scholar
Mesquita, A. and Coda, H. (2003), A two-dimensional Bem/Fem coupling applied to viscoelastic analysis of composite domains, Int. J. Numer. Meth. Eng. 57(2), pp. 251–270, 10.1002/nme.676MesquitaA.CodaH.2003A two-dimensional Bem/Fem coupling applied to viscoelastic analysis of composite domains57225127010.1002/nme.676Open DOISearch in Google Scholar
Muñoz, G. A., Sarantopoulos, Y., and Tonge, A. (1999), Complexifications of real Banach spaces, polynomials and multilinear maps, Studia Math. 134(1), pp. 1–33MuñozG. A.SarantopoulosY.TongeA.1999Complexifications of real Banach spaces, polynomials and multilinear maps134113310.4064/sm-134-1-1-33Search in Google Scholar
Näsholm, S. P. and Holm, S. (2013), On a fractional Zener elastic wave equation, Fract. Calc. Appl. Anal. 16(1), pp. 26–50, 10.2478/s13540-013-0003-1NäsholmS. P.HolmS.2013On a fractional Zener elastic wave equation161265010.2478/s13540-013-0003-1Open DOISearch in Google Scholar
Pazy, A. (1983), Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences44, Springer-Verlag, New York, 10.1007/978-1-4612-5561-1PazyA.1983Semigroups of linear operators and applications to partial differential equations44Springer-VerlagNew York10.1007/978-1-4612-5561-1Open DOISearch in Google Scholar
Perdikaris, P. and Karniadakis, G. E. (2014), Fractional-order viscoelasticity in one-dimensional blood flow models, Ann. Biomed. Eng. 42(5), pp. 1012–1023, 10.1007/s10439-014-0970-324414838PerdikarisP.KarniadakisG. E.2014Fractional-order viscoelasticity in one-dimensional blood flow models4251012102310.1007/s10439-014-0970-324414838Open DOISearch in Google Scholar
Phan-Thien, N. (2013), Understanding viscoelasticity: An introduction to Rheology, Graduate Texts in Physics, Springer-Verlag, Berlin, 10.1007/978-3-642-32958-6Phan-ThienN.2013Understanding viscoelasticity: An introduction to RheologySpringer-VerlagBerlin10.1007/978-3-642-32958-6Open DOISearch in Google Scholar
Rivière, B., Shaw, S., Wheeler, M. F., and Whiteman, J. R. (2003), Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity, Numer. Math. 95(2), pp. 347–376, 10.1007/s002110200394RivièreB.ShawS.WheelerM. F.WhitemanJ. R.2003Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity95234737610.1007/s002110200394Open DOISearch in Google Scholar
Sayas, F.-J. (2016), Retarded potentials and time domain boundary integral equations: A road map, Springer, 10.1007/978-3-319-26645-9SayasF.J.2016Springer10.1007/978-3-319-26645-9Open DOISearch in Google Scholar
Shevchenko, V. P. and Neskorodev, R. N. (2014), A numerical-analytical method for solving problems of linear viscoelasticity, Internat. Appl. Mech. 50(3), pp. 263–273, 10.1007/s10778-014-0629-7ShevchenkoV. P.NeskorodevR. N.2014A numerical-analytical method for solving problems of linear viscoelasticity50326327310.1007/s10778-014-0629-7Open DOISearch in Google Scholar
Trèves, F. (1967), Topological vector spaces, distributions and kernels, Academic Press, New York-LondonTrèvesF.1967Academic PressNew York-LondonSearch in Google Scholar
Troyani, N. and Pérez, A. (2014), A comparison of a finite element only scheme and a BEM/FEM method to compute the elastic-viscoelastic response in composite media, Finite Elem. Anal. Des. 88, pp. 42–54, 10.1016/j.finel.2014.05.003TroyaniN.PérezA.2014A comparison of a finite element only scheme and a BEM/FEM method to compute the elastic-viscoelastic response in composite media88425410.1016/j.finel.2014.05.003Open DOISearch in Google Scholar
Yu, Y., Perdikaris, P., and Karniadakis, G. E. (2016), Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms, J. Comput. Phys. 323, pp. 219–242, 10.1016/j.jcp.2016.06.03829104310YuY.PerdikarisP.KarniadakisG. E.2016Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms32321924210.1016/j.jcp.2016.06.038566890829104310Open DOISearch in Google Scholar