메뉴 건너뛰기




Volumn 133, Issue 8, 2005, Pages 2273-2282

Space-time fractional derivative operators

Author keywords

Anomalous diffusion; Evolution equation; Fractional derivative

Indexed keywords


EID: 23744477406     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-07949-9     Document Type: Article
Times cited : (58)

References (31)
  • 2
    • 0001311725 scopus 로고    scopus 로고
    • Stochastic solutions for fractional Cauchy problems
    • MR1874479 (2003d:26006)
    • B. Baeumer and M. Merschaert, Stochastic solutions for fractional Cauchy problems. Frac. Calc. Appl. Anal. 4 (2001), 481-500. MR1874479 (2003d:26006)
    • (2001) Frac. Calc. Appl. Anal. , vol.4 , pp. 481-500
    • Baeumer, B.1    Merschaert, M.2
  • 3
    • 2142701138 scopus 로고    scopus 로고
    • Limit theorems for coupled continuous time random walks
    • MR2039941 (2004m:60092)
    • P. Becker-Kern, M.M. Meerschaert and H.P. Scheffler, Limit theorems for coupled continuous time random walks. Ann. Probab. 32 (2004), No. 1B, 730-756. MR2039941 (2004m:60092)
    • (2004) Ann. Probab. , vol.32 , Issue.1 B , pp. 730-756
    • Becker-Kern, P.1    Meerschaert, M.M.2    Scheffler, H.P.3
  • 5
    • 0000914304 scopus 로고
    • Transport aspects in anomalous diffusion: Levy walks
    • A. Blumen, G. Zumofen and J. Klafter, Transport aspects in anomalous diffusion: Levy walks. Phys Rev. A 40 (1989), 3964-3973.
    • (1989) Phys Rev. A , vol.40 , pp. 3964-3973
    • Blumen, A.1    Zumofen, G.2    Klafter, J.3
  • 6
    • 0040307478 scopus 로고
    • Anomalous diffusion in disordered media - Statistical mechanisms, models and physical applications
    • MR1081295
    • J.P. Bouchaud and A. Georges, Anomalous diffusion in disordered media - statistical mechanisms, models and physical applications, Phys. Rep. 195 (1990), 127-293. MR1081295
    • (1990) Phys. Rep. , vol.195 , pp. 127-293
    • Bouchaud, J.P.1    Georges, A.2
  • 7
    • 0002745423 scopus 로고    scopus 로고
    • A fractional diffusion equation to describe Levy flights
    • MR1616103 (99a:82067)
    • A. Chaves, A fractional diffusion equation to describe Levy flights. Phys. Lett. A 239 (1998), 13-16. MR1616103 (99a:82067)
    • (1998) Phys. Lett. A , vol.239 , pp. 13-16
    • Chaves, A.1
  • 9
    • 0003513648 scopus 로고
    • Translated from the Russian, annotated, and revised by K. L. Chung. With appendices by J. L. Doob and P. L. Hsu. Revised edition, Addison-Wesley, Reading, Mass. MR0233400 (38:1722)
    • B. Gnedenko and A. Kolmogorov, Limit Distributions for Sums of Independent Random Variables. Translated from the Russian, annotated, and revised by K. L. Chung. With appendices by J. L. Doob and P. L. Hsu. Revised edition, Addison-Wesley, Reading, Mass (1968). MR0233400 (38:1722)
    • (1968) Limit Distributions for Sums of Independent Random Variables
    • Gnedenko, B.1    Kolmogorov, A.2
  • 10
    • 0002898176 scopus 로고    scopus 로고
    • Fractional calculus and continuous-time finance. III. The diffusion limit
    • Mathematical finance (Konstanz, Birkhäuser), Basel. MR1882830
    • R. Gorenflo, F. Mainardi, E. Scalas and M. Raberto, Fractional calculus and continuous-time finance. III. The diffusion limit. Mathematical finance (Konstanz, 2000), 171-180, Trends Math., Birkhäuser, Basel (2001). MR1882830
    • (2000) Trends Math. , pp. 171-180
    • Gorenflo, R.1    Mainardi, F.2    Scalas, E.3    Raberto, M.4
  • 11
    • 0003862451 scopus 로고
    • Amer. Math. Soc. Coll. Publ., American Mathematical Society, Providence. MR0089373 (19:664d)
    • E. Hille and R.S. Phillips, Functional Analysis and Semi-Groups. Amer. Math. Soc. Coll. Publ. 31, American Mathematical Society, Providence (1957). MR0089373 (19:664d)
    • (1957) Functional Analysis and Semi-groups , vol.31
    • Hille, E.1    Phillips, R.S.2
  • 13
    • 0000550285 scopus 로고
    • Stochastic pathways to anomalous diffusion
    • MR0884309 (88d:82132)
    • J. Klafter, A. Blumen and M.F. Shlesinger, Stochastic pathways to anomalous diffusion, Phys. Rev. A 35 (1987), 3081-3085. MR0884309 (88d:82132)
    • (1987) Phys. Rev. A , vol.35 , pp. 3081-3085
    • Klafter, J.1    Blumen, A.2    Shlesinger, M.F.3
  • 14
    • 0001505107 scopus 로고    scopus 로고
    • Multidimensional advection and fractional dispersion
    • M.M. Meerschaert, D. Benson and B. Bäumer, Multidimensional advection and fractional dispersion. Phys. Rev. E 59 (1999), 5026-5028.
    • (1999) Phys. Rev. E , vol.59 , pp. 5026-5028
    • Meerschaert, M.M.1    Benson, D.2    Bäumer, B.3
  • 16
    • 18344370872 scopus 로고    scopus 로고
    • Operator Lévy motion and multiscaling anomalous diffusion
    • M.M. Meerschaert, D. Benson and B. Bäumer, Operator Lévy motion and multiscaling anomalous diffusion. Phys. Rev. E 63 (2001), 1112-1117.
    • (2001) Phys. Rev. E , vol.63 , pp. 1112-1117
    • Meerschaert, M.M.1    Benson, D.2    Bäumer, B.3
  • 17
    • 3242750610 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • MR2052584
    • M.M. Meerschaert and H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times. J. Appl. Probab. 41 (2004), No. 2, 455-466. MR2052584
    • (2004) J. Appl. Probab. , vol.41 , Issue.2 , pp. 455-466
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 18
    • 41349099804 scopus 로고    scopus 로고
    • Stochastic solution of space-time fractional diffusion equations
    • MR1917983 (2003d:60165)
    • M.M. Meerschaert, D.A. Benson, H.P. Scheffler and B. Baeumer, Stochastic solution of space-time fractional diffusion equations. Phys. Rev. E 65 (2002), 1103-1106. MR1917983 (2003d:60165)
    • (2002) Phys. Rev. E , vol.65 , pp. 1103-1106
    • Meerschaert, M.M.1    Benson, D.A.2    Scheffler, H.P.3    Baeumer, B.4
  • 20
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • MR1809268 (2001k:82082)
    • Metzler R. and J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep. 339 (2000), 1-77. MR1809268 (2001k:82082)
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 22
    • 0002567920 scopus 로고
    • Random walks on lattices. II
    • MR0172344 (30:2563)
    • E.W. Montroll and G.H. Weiss, Random walks on lattices. II. J. Mathematical Phys. 6 (1965), 167-181. MR0172344 (30:2563)
    • (1965) J. Mathematical Phys. , vol.6 , pp. 167-181
    • Montroll, E.W.1    Weiss, G.H.2
  • 24
    • 0036949980 scopus 로고    scopus 로고
    • Waiting-times and returns in high-frequency financial data: An empirical study
    • M. Raberto, E. Scalas and F. Mainardi, Waiting-times and returns in high-frequency financial data: an empirical study. Physica A 314 (2002), 749-755.
    • (2002) Physica A , vol.314 , pp. 749-755
    • Raberto, M.1    Scalas, E.2    Mainardi, F.3
  • 25
    • 0042808444 scopus 로고    scopus 로고
    • Waiting time distributions in financial markets
    • MR1930869
    • L. Sabatelli, S. Keating, J. Dudley, P. Richmond, Waiting time distributions in financial markets. Eur. Phys. J B 27 (2002), 273-275. MR1930869
    • (2002) Eur. Phys. J B , vol.27 , pp. 273-275
    • Sabatelli, L.1    Keating, S.2    Dudley, J.3    Richmond, P.4
  • 26
    • 0000599032 scopus 로고    scopus 로고
    • Fractional kinetic equations: Solutions and applications
    • MR1604710 (98k:82162)
    • A.I. Saichev and G.M. Zaslavsky, Fractional kinetic equations: Solutions and applications. Chaos 7 (1997), 753-764. MR1604710 (98k:82162)
    • (1997) Chaos , vol.7 , pp. 753-764
    • Saichev, A.I.1    Zaslavsky, G.M.2
  • 28
    • 0034275979 scopus 로고    scopus 로고
    • Fractional calculus and continuous-time finance
    • MR1773804 (2001d:91104)
    • E. Scalas, R. Gorenflo and F. Mainardi, Fractional calculus and continuous-time finance. Phys. A 284 (2000), 376-384. MR1773804 (2001d:91104)
    • (2000) Phys. A , vol.284 , pp. 376-384
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3
  • 29
    • 35949027117 scopus 로고
    • Stochastic transport in a disordered solid. I. Theory
    • MR0391854 (52:12673)
    • H. Scher and M. Lax, Stochastic transport in a disordered solid. I. Theory. Phys. Rev. B 7 (1973), 4491-4502. MR0391854 (52:12673)
    • (1973) Phys. Rev. B , vol.7 , pp. 4491-4502
    • Scher, H.1    Lax, M.2
  • 31
    • 43949160116 scopus 로고
    • Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion
    • MR1295881 (95h:58120)
    • G. Zaslavsky, Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion. Phys. D 76 (1994), 110-122. MR1295881 (95h:58120)
    • (1994) Phys. D , vol.76 , pp. 110-122
    • Zaslavsky, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.