메뉴 건너뛰기




Volumn 465, Issue 2106, 2009, Pages 1893-1917

Time distributed-order diffusion-wave equation. Ii. Applications of laplace and fourier transformations

Author keywords

Diffusion wave equation; Distributed order fractional derivative; Distributional diffusion wave equation; Fractional derivative

Indexed keywords

DIFFUSION; FOURIER ANALYSIS; FUNCTION EVALUATION; GREEN'S FUNCTION; TELEGRAPH;

EID: 67149125441     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0446     Document Type: Article
Times cited : (93)

References (30)
  • 1
    • 22544474172 scopus 로고    scopus 로고
    • On a fractional distributed-order oscillator
    • doi:10.1088/0305-4470/38/30/006
    • Atanackovic, T. M., Budincevic, M. and Pilipovic, S. 2005 On a fractional distributed-order oscillator. J. Phys. A Math. Gen. 38, 6703-6713. (doi:10.1088/0305-4470/38/30/006)
    • (2005) J. Phys. A Math. Gen , vol.38 , pp. 6703-6713
    • Atanackovic, T.M.1    Budincevic, M.2    Pilipovic, S.3
  • 2
    • 34247636164 scopus 로고    scopus 로고
    • Diffusion wave equation with two fractional derivatives of different order
    • doi:10.1088/1751-8113/40 /20/006
    • Atanackovic, T. M., Pilipovic, S. and Zorica, D. 2007 Diffusion wave equation with two fractional derivatives of different order. J. Phys. A Math. Theor. 40, 5319-5333. (doi:10.1088/1751-8113/40 /20/006)
    • (2007) J. Phys. A Math. Theor , vol.40 , pp. 5319-5333
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 3
    • 61949113544 scopus 로고    scopus 로고
    • Distributional framework for solving fractional differential equations
    • doi:10.1080/10652460 802568069
    • Atanackovic, T. M., Oparnica, L. and Pilipovic, S. 2009 Distributional framework for solving fractional differential equations. Integral Transforms Special Funct. 20, 215-222. (doi:10.1080/10652460 802568069)
    • (2009) Integral Transforms Special Funct , vol.20 , pp. 215-222
    • Atanackovic, T.M.1    Oparnica, L.2    Pilipovic, S.3
  • 4
    • 67149103784 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. I. Volterra-type equation
    • doi:10.1098/rspa.2008.0445
    • Atanackovic, T. M., Pilipovic, S. and Zorica, D. 2009 Time distributed-order diffusion-wave equation. I. Volterra-type equation. Proc. R. Soc. A 465, 1869-1891. (doi:10.1098/rspa.2008.0445)
    • (2009) Proc. R. Soc. A , vol.465 , pp. 1869-1891
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 5
    • 41349088572 scopus 로고    scopus 로고
    • Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations
    • doi:10.1103/PhysRevE.66.046129
    • Chechkin, A. V., Gorenflo, R. and Sokolov, I. M. 2002 Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. Phys. Rev. E 66, 046129. (doi:10.1103/PhysRevE.66.046129)
    • (2002) Phys. Rev. E , vol.66 , pp. 046129
    • Chechkin, A.V.1    Gorenflo, R.2    Sokolov, I.M.3
  • 6
    • 0037092904 scopus 로고    scopus 로고
    • Analytical and numerical inversion of the Laplace-Carson transform by a differential method
    • doi:10.1016/S0010-4655 (02) 00281-3
    • Donalto, C. 2002 Analytical and numerical inversion of the Laplace-Carson transform by a differential method. Comput. Phys. Commun. 145, 298-309. (doi:10.1016/S0010-4655 (02) 00281-3)
    • (2002) Comput. Phys. Commun , vol.145 , pp. 298-309
    • Donalto, C.1
  • 7
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • doi:10.1016/j.jde.2003.12.002
    • Eidelman, S. D. and Kochubei, A. N. 2004 Cauchy problem for fractional diffusion equations. J. Differ. Eqns. 199, 211-255. (doi:10.1016/j.jde.2003.12.002)
    • (2004) J. Differ. Eqns , vol.199 , pp. 211-255
    • Eidelman, S.D.1    Kochubei, A.N.2
  • 8
    • 0032165073 scopus 로고    scopus 로고
    • Improvement of accuracy in numerical methods for inverting Laplace transforms based on Post-Widder formula
    • S0898-1221 (98) 00147-3, doi:10.1016
    • Frolov, G. A. and Kitaev, M. Y. 1998 Improvement of accuracy in numerical methods for inverting Laplace transforms based on Post-Widder formula. Comput. Math. Appl. 36, 23-34. (doi:10.1016 /S0898-1221 (98) 00147-3)
    • (1998) Comput. Math. Appl , vol.36 , pp. 23-34
    • Frolov, G.A.1    Kitaev, M.Y.2
  • 9
    • 34547639814 scopus 로고    scopus 로고
    • Multidimensional solutions of space-fractional diffusion equations
    • doi:10.1098/rspa.2001.0849
    • Hanyga, A. 2001 Multidimensional solutions of space-fractional diffusion equations. Proc. R. Soc. Lond. A 457, 2993-3005. (doi:10.1098/rspa.2001.0849)
    • (2001) Proc. R. Soc. Lond. A , vol.457 , pp. 2993-3005
    • Hanyga, A.1
  • 10
    • 34249011674 scopus 로고    scopus 로고
    • Multi-dimensional solutions of space-time-fractional diffusion equations
    • doi:10.1098/rspa.2001.0893
    • Hanyga, A. 2002a Multi-dimensional solutions of space-time-fractional diffusion equations. Proc. R. Soc. Lond. A 458, 429-450. (doi:10.1098/rspa.2001.0893)
    • (2002) Proc. R. Soc. Lond. A , vol.458 , pp. 429-450
    • Hanyga, A.1
  • 11
    • 57249098754 scopus 로고    scopus 로고
    • Multidimensional solutions of time-fractional diffusion-wave equations
    • doi:10.1098/rspa.2001.0904
    • Hanyga, A. 2002b Multidimensional solutions of time-fractional diffusion-wave equations. Proc. R. Soc. Lond. A 458, 933-957. (doi:10.1098/rspa.2001.0904)
    • (2002) Proc. R. Soc. Lond. A , vol.458 , pp. 933-957
    • Hanyga, A.1
  • 12
    • 34248206059 scopus 로고    scopus 로고
    • Anomalous diffusion without scale invariance
    • doi:10.1088/1751-8113/40/21/007
    • Hanyga, A. 2007 Anomalous diffusion without scale invariance. J. Phys. A Math. Theor. 40, 5551-5563. (doi:10.1088/1751-8113/40/21/007)
    • (2007) J. Phys. A Math. Theor , vol.40 , pp. 5551-5563
    • Hanyga, A.1
  • 13
    • 37449011239 scopus 로고    scopus 로고
    • Distributed order calculus and equations of ultraslow diffusion
    • doi:10.1016/j.jmaa.2007.08.024
    • Kochubei, A. N. 2008 Distributed order calculus and equations of ultraslow diffusion. J. Math. Anal. Appl. 340, 252-281. (doi:10.1016/j.jmaa.2007.08.024)
    • (2008) J. Math. Anal. Appl , vol.340 , pp. 252-281
    • Kochubei, A.N.1
  • 14
    • 33646371459 scopus 로고    scopus 로고
    • Solution of a modified fractional diffusion equation
    • doi:10.1016/j.physa.2005.12. 012
    • Langlands, T. A. M. 2006 Solution of a modified fractional diffusion equation. Physica A 367, 136-144. (doi:10.1016/j.physa.2005.12. 012)
    • (2006) Physica A , vol.367 , pp. 136-144
    • Langlands, T.A.M.1
  • 15
    • 56549085438 scopus 로고    scopus 로고
    • Maximum principle for the generalized time-fractional diffusion equation
    • doi:10.1016/j.jmaa.2008.10.018
    • Luchko, Y. 2009 Maximum principle for the generalized time-fractional diffusion equation. J. Math. Anal. Appl. 351, 218-223. (doi:10.1016/j.jmaa.2008.10.018)
    • (2009) J. Math. Anal. Appl , vol.351 , pp. 218-223
    • Luchko, Y.1
  • 16
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion wave phenomena
    • doi:10.1016/0960-0779 (95) 00125-5
    • Mainardi, F. 1996 Fractional relaxation-oscillation and fractional diffusion wave phenomena. Chaos Solitons Fractals 7, 1461-1477. (doi:10.1016/0960-0779 (95) 00125-5)
    • (1996) Chaos Solitons Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 17
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • Fractals and fractional calculus in continuum mechanics eds A. Carpinteri and F. Mainardi, Berlin, Germany: Springer
    • Mainardi, F. 1997 Fractional calculus: some basic problems in continuum and statistical mechanics. In Fractals and fractional calculus in continuum mechanics (eds A. Carpinteri and F. Mainardi). CISM Courses and Lecture Notes, no. 378, pp. 291-348. Berlin, Germany: Springer.
    • (1997) CISM Courses and Lecture Notes , vol.378 , pp. 291-348
    • Mainardi, F.1
  • 18
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi, F., Luchko, Y. and Pagnini, G. 2001 The fundamental solution of the space-time fractional diffusion equation. Fract. Calculus Appl. Anal. 4, 153-192.
    • (2001) Fract. Calculus Appl. Anal , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 19
    • 34247367101 scopus 로고    scopus 로고
    • Some aspects of fractional diffusion equations of single and distributed order
    • doi:10.1016/j.amc.2006.08.126
    • Mainardi, F., Pagnini, G. and Gorenflo, R. 2007a Some aspects of fractional diffusion equations of single and distributed order. Appl. Math. Comput. 187, 295-305. (doi:10.1016/j.amc.2006.08.126)
    • (2007) Appl. Math. Comput , vol.187 , pp. 295-305
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 20
    • 34748907169 scopus 로고    scopus 로고
    • The two forms of fractional relaxation of distributed order
    • doi:10.1177/1077546307077468
    • Mainardi, F., Mura, A., Gorenflo, R. and Stojanovic, M. 2007b The two forms of fractional relaxation of distributed order. J. Vib. Control. 13, 1249-1268. (doi:10.1177/1077546307077468)
    • (2007) J. Vib. Control , vol.13 , pp. 1249-1268
    • Mainardi, F.1    Mura, A.2    Gorenflo, R.3    Stojanovic, M.4
  • 21
    • 52349083860 scopus 로고    scopus 로고
    • Time-fractional diffusion of distributed order
    • Mainardi, F., Pagnini, G., Mura, A. and Gorenflo, R. 2008 Time-fractional diffusion of distributed order. J. Vib. Control 14, 1267-1290. (http://arXiv.org/abs/cond-mat/0701132)
    • (2008) J. Vib. Control , vol.14 , pp. 1267-1290
    • Mainardi, F.1    Pagnini, G.2    Mura, A.3    Gorenflo, R.4
  • 22
    • 4544299160 scopus 로고    scopus 로고
    • Distributed order fractional sub-diffusion
    • doi:10.1142 /S0218348X04002410
    • Naber, M. 2004 Distributed order fractional sub-diffusion. Fractals 12, 23-32. (doi:10.1142 /S0218348X04002410)
    • (2004) Fractals , vol.12 , pp. 23-32
    • Naber, M.1
  • 30
    • 33745194344 scopus 로고    scopus 로고
    • New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation
    • doi:10.1016/j.chaos.2005.08.151
    • Yu, R. and Zhang, H. 2006 New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation. Chaos Solitons Fractals 30, 946-955. (doi:10.1016/j.chaos.2005.08.151)
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 946-955
    • Yu, R.1    Zhang, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.