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Volumn 70, Issue 2, 2012, Pages 1273-1281

Stochastic solution to a time-fractional attenuated wave equation

Author keywords

Complex media; Fractional derivative; Inverse subordinator; Stable law; Wave equation

Indexed keywords

CAUSAL SOLUTIONS; COMPLEX MEDIA; COMPLEX NONLINEAR DYNAMICS; FRACTIONAL DERIVATIVES; FRACTIONAL WAVE EQUATION; MEDICAL ULTRASOUND; RANDOM WALK MODELS; STABLE LAW; STOCHASTIC SOLUTION; SUBORDINATORS;

EID: 84871013921     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0532-x     Document Type: Article
Times cited : (16)

References (30)
  • 2
    • 43949160116 scopus 로고
    • Fractional kinetic equation for Hamiltonian chaos
    • Zaslavsky, G.: Fractional kinetic equation for Hamiltonian chaos. Physica D 76, 110-122 (1994)
    • (1994) Physica D , vol.76 , pp. 110-122
    • Zaslavsky, G.1
  • 3
    • 34748827947 scopus 로고    scopus 로고
    • Fractional Euler-Lagrange equations of motion in fractional space
    • Muslih, S.I., Baleanu, D.: Fractional Euler-Lagrange equations of motion in fractional space. J. Vib. Control 13(9- 10), 1209-1216 (2007)
    • (2007) J. Vib. Control , vol.13 , Issue.9-10 , pp. 1209-1216
    • Muslih, S.I.1    Baleanu, D.2
  • 4
    • 79960532588 scopus 로고    scopus 로고
    • Wave simulation in dissipative media described by distributed-order fractional time derivatives
    • Caputo, M., Carcione, J.M.: Wave simulation in dissipative media described by distributed-order fractional time derivatives. J. Vib. Control 17(8), 1121-1130 (2011)
    • (2011) J. Vib. Control , vol.17 , Issue.8 , pp. 1121-1130
    • Caputo, M.1    Carcione, J.M.2
  • 5
    • 84863972983 scopus 로고    scopus 로고
    • Fractional Euler-Lagrange equations revisited
    • Herzallah, M., Baleanu, D.: Fractional Euler-Lagrange equations revisited. Nonlinear Dyn. 69(3), 977-982 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , Issue.3 , pp. 977-982
    • Herzallah, M.1    Baleanu, D.2
  • 6
    • 84878363605 scopus 로고    scopus 로고
    • A fractional calculus based model for the simulation of an outbreak of dengue fever
    • to appear, doi:10.1007/s11071-012-0475-2
    • Diethelm, K.: A fractional calculus based model for the simulation of an outbreak of dengue fever. Nonlinear Dyn. (2012, to appear). doi:10.1007/s11071- 012-0475-2
    • (2012) Nonlinear Dyn.
    • Diethelm, K.1
  • 7
    • 0028292355 scopus 로고
    • Time domain wave equations for lossy media obeying a frequency power law
    • Szabo, T.L.: Time domain wave equations for lossy media obeying a frequency power law. J. Acoust. Soc. Am. 96, 491-500 (1994)
    • (1994) J. Acoust. Soc. Am. , vol.96 , pp. 491-500
    • Szabo, T.L.1
  • 8
    • 56749132453 scopus 로고    scopus 로고
    • Analytical time-domain Green's functions for power-law media
    • Kelly, J.F., McGough, R.J., Meerschaert, M.M.: Analytical time-domain Green's functions for power-law media. J. Acoust. Soc. Am. 124(5), 2861-2872 (2008)
    • (2008) J. Acoust. Soc. Am. , vol.124 , Issue.5 , pp. 2861-2872
    • Kelly, J.F.1    McGough, R.J.2    Meerschaert, M.M.3
  • 9
    • 67651103488 scopus 로고    scopus 로고
    • Existence results for differential equations with fractional order and impulses
    • Agarwal, R.P., Benchohra, M., Slimani, B.A.: Existence results for differential equations with fractional order and impulses. Mem. Differ. Equ. Math. Phys. 44, 1-21 (2008)
    • (2008) Mem. Differ. Equ. Math. Phys. , vol.44 , pp. 1-21
    • Agarwal, R.P.1    Benchohra, M.2    Slimani, B.A.3
  • 10
    • 41349099804 scopus 로고    scopus 로고
    • Stochastic solution of space-time fractional diffusion equations
    • Meerschaert, M.M., Benson, D.A., Scheffler, H.-P., Baeumer, B.: Stochastic solution of space-time fractional diffusion equations. Phys. Rev. E 65, 1103-1106 (2002)
    • (2002) Phys. Rev. e , vol.65 , pp. 1103-1106
    • Meerschaert, M.M.1    Benson, D.A.2    Scheffler, H.-P.3    Baeumer, B.4
  • 11
    • 0242693197 scopus 로고    scopus 로고
    • Modified Szabo's wave equation models for lossy media obeying frequency power law
    • Chen,W., Holm, S.: Modified Szabo's wave equation models for lossy media obeying frequency power law. J. Acoust. Soc. Am. 114, 2570-2754 (2003)
    • (2003) J. Acoust. Soc. Am. , vol.114 , pp. 2570-2754
    • Chen, W.1    Holm, S.2
  • 12
    • 9644281076 scopus 로고    scopus 로고
    • Full wave modeling of therapeutic ultrasound: Efficient timedomain implementation of the frequency power-law attenuation
    • Liebler, M., Ginter, S., Dreyer, T., Riedlinger, R.E.: Full wave modeling of therapeutic ultrasound: efficient timedomain implementation of the frequency power-law attenuation. J. Acoust. Soc. Am. 116, 2742-2750 (2004)
    • (2004) J. Acoust. Soc. Am. , vol.116 , pp. 2742-2750
    • Liebler, M.1    Ginter, S.2    Dreyer, T.3    Riedlinger, R.E.4
  • 13
    • 0011032162 scopus 로고
    • Transient solution for sound radiated into a viscous fluid
    • Blackstock, D.T.: Transient solution for sound radiated into a viscous fluid. J. Acoust. Soc. Am. 41, 1312-1319 (1967)
    • (1967) J. Acoust. Soc. Am. , vol.41 , pp. 1312-1319
    • Blackstock, D.T.1
  • 15
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • Meerschaert, M.M., Scheffler, H.-P.: Limit theorems for continuous time random walks with infinite mean waiting times. J. Appl. Probab. 41(3), 623-638 (2004)
    • (2004) J. Appl. Probab. , vol.41 , Issue.3 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 16
    • 18944388435 scopus 로고    scopus 로고
    • Fractal travel time estimates for dispersive contaminants
    • Clarke, D.D., Meerschaert, M.M., Wheatcraft, S.W.: Fractal travel time estimates for dispersive contaminants. Ground Water 43(3), 401-407 (2005)
    • (2005) Ground Water , vol.43 , Issue.3 , pp. 401-407
    • Clarke, D.D.1    Meerschaert, M.M.2    Wheatcraft, S.W.3
  • 18
    • 73549104035 scopus 로고    scopus 로고
    • Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics
    • Kolokoltsov, V.N.: Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Theory Probab. Appl. 53(4), 594-609 (2009)
    • (2009) Theory Probab. Appl. , vol.53 , Issue.4 , pp. 594-609
    • Kolokoltsov, V.N.1
  • 19
    • 14844311252 scopus 로고    scopus 로고
    • Advection and dispersion in time and space
    • Baeumer, B., Benson, D.A.,Meerschaert, M.M.: Advection and dispersion in time and space. Phys. A 350(2-4), 245- 262 (2005)
    • (2005) Phys. A , vol.350 , Issue.2-4 , pp. 245-262
    • Baeumer, B.1    Benson, D.A.2    Meerschaert, M.M.3
  • 20
    • 0000599032 scopus 로고    scopus 로고
    • Fractional kinetic equations: Solutions and applications
    • Saichev, A.I., Zaslavsky, G.M.: Fractional kinetic equations: solutions and applications. Chaos 7(4), 753-764 (1997)
    • (1997) Chaos , vol.7 , Issue.4 , pp. 753-764
    • Saichev, A.I.1    Zaslavsky, G.M.2
  • 22
    • 48349113290 scopus 로고    scopus 로고
    • Triangular array limits for continuous time random walks
    • Meerschaert, M.M., Scheffler, H.-P.: Triangular array limits for continuous time random walks. Stoch. Process. Appl. 118(9), 1606-1633 (2008)
    • (2008) Stoch. Process. Appl. , vol.118 , Issue.9 , pp. 1606-1633
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 24
    • 33751033123 scopus 로고    scopus 로고
    • Fractional diffusion with two time scales
    • Baeumer, B., Meerschaert, M.M.: Fractional diffusion with two time scales. Physica A 373, 237-251 (2007)
    • (2007) Physica A , vol.373 , pp. 237-251
    • Baeumer, B.1    Meerschaert, M.M.2
  • 26
    • 3242750610 scopus 로고    scopus 로고
    • Limit theorem for continuous-time random walks with two time scales
    • Meerschaert, M.M., Scheffler, H.-P., Kern, P.: Limit theorem for continuous-time random walks with two time scales. J. Appl. Probab. 41(2), 455-466 (2004)
    • (2004) J. Appl. Probab. , vol.41 , Issue.2 , pp. 455-466
    • Meerschaert, M.M.1    Scheffler, H.-P.2    Kern, P.3
  • 27
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent-II
    • Caputo, M.: Linear models of dissipation whose Q is almost frequency independent-II. Geophys. J. R. Astron. Soc. 13(5), 529-539 (1967)
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , Issue.5 , pp. 529-539
    • Caputo, M.1
  • 28
    • 33845373149 scopus 로고    scopus 로고
    • Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation
    • Wismer, M.G.: Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation. J. Acoust. Soc. Am. 120, 3493-3502 (2006)
    • (2006) J. Acoust. Soc. Am. , vol.120 , pp. 3493-3502
    • Wismer, M.G.1
  • 29
    • 1642641759 scopus 로고    scopus 로고
    • Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency
    • Chen, W., Holm, S.: Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency. J. Acoust. Soc. Am. 115, 1424-1430 (2004)
    • (2004) J. Acoust. Soc. Am. , vol.115 , pp. 1424-1430
    • Chen, W.1    Holm, S.2
  • 30
    • 77956256476 scopus 로고    scopus 로고
    • Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian
    • Treeby, B.E., Cox, B.T.: Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian. J. Acoust. Soc. Am. 127, 2741-2748 (2010)
    • (2010) J. Acoust. Soc. Am. , vol.127 , pp. 2741-2748
    • Treeby, B.E.1    Cox, B.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.