메뉴 건너뛰기




Volumn 21, Issue 4, 2007, Pages 163-174

The fractional Chapman-Kolmogorov equation

Author keywords

Chapman Kolmogorov equation; Fractal; Fractional integral

Indexed keywords


EID: 33947140425     PISSN: 02179849     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217984907012712     Document Type: Article
Times cited : (10)

References (40)
  • 2
    • 85039223316 scopus 로고    scopus 로고
    • or Fractional Integrals and Derivatives Theory and Applications (Gordon and Breach, New York, 1993).
    • or Fractional Integrals and Derivatives Theory and Applications (Gordon and Breach, New York, 1993).
  • 3
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • G. M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Phys. Rep. 371 (2002) 461.
    • (2002) Phys. Rep , vol.371 , pp. 461
    • Zaslavsky, G.M.1
  • 6
    • 13444252540 scopus 로고    scopus 로고
    • Continuous medium model for fractal media
    • V. E. Tarasov, Continuous medium model for fractal media, Phys. Lett. A 336 (2005) 167;
    • (2005) Phys. Lett. A , vol.336 , pp. 167
    • Tarasov, V.E.1
  • 7
    • 20444386984 scopus 로고    scopus 로고
    • Fractional hydrodynamic equations for fractal media
    • Fractional hydrodynamic equations for fractal media, Ann. Phys. 318 (2005) 286;
    • (2005) Ann. Phys , vol.318 , pp. 286
  • 8
    • 20444395073 scopus 로고    scopus 로고
    • Possible experimental test of continuous medium model for fractal media
    • Possible experimental test of continuous medium model for fractal media, Phys. Lett. A 341 (2005) 467;
    • (2005) Phys. Lett. A , vol.341 , pp. 467
  • 9
    • 23844432993 scopus 로고    scopus 로고
    • Wave equation for fractal solid string
    • Wave equation for fractal solid string, Mod. Phys. Lett. B 19 (2005) 721;
    • (2005) Mod. Phys. Lett. B , vol.19 , pp. 721
  • 10
    • 27544489901 scopus 로고    scopus 로고
    • Dynamics of fractal solid
    • Dynamics of fractal solid, Int. J. Mod. Phys. B. 19 (2005) 4103.
    • (2005) Int. J. Mod. Phys. B , vol.19 , pp. 4103
  • 11
    • 19944384253 scopus 로고    scopus 로고
    • Fractional Ginzburg-Landau equation for fractal media
    • V. E. Tarasov and G. M. Zaslavsky, Fractional Ginzburg-Landau equation for fractal media, Physica A 354 (2005) 249.
    • (2005) Physica A , vol.354 , pp. 249
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 12
    • 43949160116 scopus 로고
    • Fractional kinetic equation for Hamiltonian chaos
    • G. M. Zaslavsky, Fractional kinetic equation for Hamiltonian chaos, Physica D 76 (1994) 110.
    • (1994) Physica D , vol.76 , pp. 110
    • Zaslavsky, G.M.1
  • 13
    • 0000599032 scopus 로고    scopus 로고
    • Fractional kinetic equations: Solutions and applications
    • A. I. Saichev and G. M. Zaslavsky, Fractional kinetic equations: Solutions and applications, Chaos 7 (1997) 753.
    • (1997) Chaos , vol.7 , pp. 753
    • Saichev, A.I.1    Zaslavsky, G.M.2
  • 14
    • 0035679868 scopus 로고    scopus 로고
    • Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model
    • B. A. Carreras, V. E. Lynch and G. M. Zaslavsky, Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model, Physics of Plasmas 8 (2001) 5096.
    • (2001) Physics of Plasmas , vol.8 , pp. 5096
    • Carreras, B.A.1    Lynch, V.E.2    Zaslavsky, G.M.3
  • 15
    • 10844294194 scopus 로고    scopus 로고
    • Fractal topology and strange kinetics: From percolation theory to problems in cosmic electrodynamics
    • L. M. Zelenyi and A. V. Milovanov, Fractal topology and strange kinetics: From percolation theory to problems in cosmic electrodynamics, Physics Uspekhi 47 (2004) 749.
    • (2004) Physics Uspekhi , vol.47 , pp. 749
    • Zelenyi, L.M.1    Milovanov, A.V.2
  • 16
    • 24344459045 scopus 로고    scopus 로고
    • Electromagnetic field of fractal distribution of charged particles
    • V. E. Tarasov, Electromagnetic field of fractal distribution of charged particles, Physics of Plasmas 12 (2005) 082106;
    • (2005) Physics of Plasmas , vol.12 , pp. 082106
    • Tarasov, V.E.1
  • 17
    • 27344442012 scopus 로고    scopus 로고
    • Multipole moments of fractal distribution of charges
    • Multipole moments of fractal distribution of charges, Mod. Phys. Lett. B 19 (2005) 1107;
    • (2005) Mod. Phys. Lett. B , vol.19 , pp. 1107
  • 18
    • 33744819200 scopus 로고    scopus 로고
    • Magnetohydrodynamics of fractal media
    • Magnetohydrodynamics of fractal media, Physics of Plasmas 13 (2006) 052107.
    • (2006) Physics of Plasmas , vol.13 , pp. 052107
  • 19
    • 32944461493 scopus 로고    scopus 로고
    • Gravitational field of fractal distribution of particles
    • V. E. Tarasov, Gravitational field of fractal distribution of particles, Celes. Mech. Dynam. Astron. 19 (2006) 1.
    • (2006) Celes. Mech. Dynam. Astron , vol.19 , pp. 1
    • Tarasov, V.E.1
  • 20
    • 0000145521 scopus 로고    scopus 로고
    • On Mittag-Leffler-type functions in fractional evolution processes
    • F. Mainardi and R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes, J. Comput. Appl. Math. 118 (2000) 283.
    • (2000) J. Comput. Appl. Math , vol.118 , pp. 283
    • Mainardi, F.1    Gorenflo, R.2
  • 21
    • 33744831468 scopus 로고    scopus 로고
    • Dynamics with low-level fractionality
    • V. E. Tarasov and G. M. Zaslavsky, Dynamics with low-level fractionality, Physica A 368 (2006) 399.
    • (2006) Physica A , vol.368 , pp. 399
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 22
    • 1842535435 scopus 로고    scopus 로고
    • Fractional generalization of Liouville equation
    • V. E. Tarasov, Fractional generalization of Liouville equation, Chaos 14 (2004) 123;
    • (2004) Chaos , vol.14 , pp. 123
    • Tarasov, V.E.1
  • 23
    • 41349084525 scopus 로고    scopus 로고
    • Fractional systems and fractional Bogoliubov hierarchy equations
    • Fractional systems and fractional Bogoliubov hierarchy equations, Phys. Rev. E 71 (2005) 011102;
    • (2005) Phys. Rev. E , vol.71 , pp. 011102
  • 24
    • 20444376273 scopus 로고    scopus 로고
    • Fractional Liouville and BBGKI equations
    • Fractional Liouville and BBGKI equations, J. Phys. Conf. Ser. 7 (2005) 17;
    • (2005) J. Phys. Conf. Ser , vol.7 , pp. 17
  • 25
    • 32644440042 scopus 로고    scopus 로고
    • Transport equations from Liouville equations for fractional systems
    • Transport equations from Liouville equations for fractional systems, Int. J. Mod. Phys. B. 20 (2006) 341.
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 341
  • 26
    • 21244457230 scopus 로고    scopus 로고
    • Fractional generalization of gradient and Hamiltonian systems
    • V. E. Tarasov, Fractional generalization of gradient and Hamiltonian systems, J. Phys. A 38 (2005) 5929;
    • (2005) J. Phys. A , vol.38 , pp. 5929
    • Tarasov, V.E.1
  • 27
    • 24144492386 scopus 로고    scopus 로고
    • Fractional generalization of gradient systems
    • Fractional generalization of gradient systems, Lett. Math. Phys. 73 (2005) 49;
    • (2005) Lett. Math. Phys , vol.73 , pp. 49
  • 28
    • 33745314459 scopus 로고    scopus 로고
    • Fractional variations for dynamical systems: Hamilton and Lagrange approaches
    • Fractional variations for dynamical systems: Hamilton and Lagrange approaches, Journal of Physics A 39 (2006) 8409.
    • (2006) Journal of Physics A , vol.39 , pp. 8409
  • 29
    • 33646823954 scopus 로고    scopus 로고
    • Nonlinear fractional dynamics of lattice with long-range interaction
    • N. Laskin and G. M. Zaslavsky, Nonlinear fractional dynamics of lattice with long-range interaction, Physica A 368 (2006) 38.
    • (2006) Physica A , vol.368 , pp. 38
    • Laskin, N.1    Zaslavsky, G.M.2
  • 30
    • 33744801927 scopus 로고    scopus 로고
    • Fractional dynamics of coupled oscillators with long-range interaction
    • V. E. Tarasov and G. M. Zaslavsky, Fractional dynamics of coupled oscillators with long-range interaction, Chaos 16 (2006) 023110;
    • (2006) Chaos , vol.16 , pp. 023110
    • Tarasov, V.E.1    Zaslavsky, G.M.2
  • 31
    • 33646938767 scopus 로고    scopus 로고
    • Fractional dynamics of systems with long-range interaction
    • Fractional dynamics of systems with long-range interaction, Commun. Nonlin. Sci. Numer. Simul. 11 (2006) 885.
    • (2006) Commun. Nonlin. Sci. Numer. Simul , vol.11 , pp. 885
  • 32
    • 33745306633 scopus 로고    scopus 로고
    • Coupled oscillators with power-law interaction and their fractional dynamics analogues
    • accepted E-print math-ph/0603074
    • N. Korabel, G. M. Zaslavsky and V. E. Tarasov, Coupled oscillators with power-law interaction and their fractional dynamics analogues, Commun. Nonlin. Sci. Numer. Simul. 11 (2006) accepted E-print math-ph/0603074.
    • (2006) Commun. Nonlin. Sci. Numer. Simul , vol.11
    • Korabel, N.1    Zaslavsky, G.M.2    Tarasov, V.E.3
  • 33
    • 0003787842 scopus 로고
    • Cambridge University Press, Cambridge, Sec. 4
    • J. C. Collins, Renormalization (Cambridge University Press, Cambridge, 1984), Sec. 4.
    • (1984) Renormalization
    • Collins, J.C.1
  • 34
    • 0010460408 scopus 로고
    • Quantum field theory on fractal spacetime: A new regularization method
    • K. Svozil, Quantum field theory on fractal spacetime: A new regularization method, J. Phys. A 20 (1987) 3861.
    • (1987) J. Phys. A , vol.20 , pp. 3861
    • Svozil, K.1
  • 36
    • 0000189685 scopus 로고
    • Uber die analytischen Methoden in der Wahrschenlichkeitsrechnung
    • A. Kolmogoroff, Uber die analytischen Methoden in der Wahrschenlichkeitsrechnung, Math. Ann. 104 (1931) 415.
    • (1931) Math. Ann , vol.104 , pp. 415
    • Kolmogoroff, A.1
  • 37
    • 0002837644 scopus 로고
    • On analytic methods in probability theory
    • A. N. Kolmogorov, On analytic methods in probability theory, Uspehi Mat. Nauk 5 (1938) 5.
    • (1938) Uspehi Mat. Nauk , vol.5 , pp. 5
    • Kolmogorov, A.N.1
  • 39
    • 0004122682 scopus 로고    scopus 로고
    • 2nd edn, Cambridge, Cambridge University Press
    • C. A. Rogers, Hausdorff Measures, 2nd edn. (Cambridge, Cambridge University Press, 1999).
    • (1999) Hausdorff Measures
    • Rogers, C.A.1
  • 40
    • 33750493372 scopus 로고
    • Quantum field-theory model in less than 4 dimensions
    • K. G. Wilson, Quantum field-theory model in less than 4 dimensions, Phys. Rev. D 7 (1973) 2911.
    • (1973) Phys. Rev. D , vol.7 , pp. 2911
    • Wilson, K.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.