메뉴 건너뛰기




Volumn 50, Issue 6, 2009, Pages

Solution of the fractional Langevin equation and the Mittag-Leffler functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 67650479716     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3152608     Document Type: Article
Times cited : (47)

References (30)
  • 1
    • 4043164644 scopus 로고    scopus 로고
    • Investigation on anomalous diffusion for nuclear fusion reaction
    • 0556-2813,. 10.1103/PhysRevC.67.064606
    • Bao, J. D. and Zhuo, Y. Z., " Investigation on anomalous diffusion for nuclear fusion reaction.," Phys. Rev. C 0556-2813 67, 064606 (2003). 10.1103/PhysRevC.67.064606
    • (2003) Phys. Rev. C , vol.67 , pp. 064606
    • Bao, J.D.1    Zhuo, Y.Z.2
  • 2
    • 79051471302 scopus 로고    scopus 로고
    • Two-point correlation function of the fractional Ornstein-Uhlenbeck process
    • 0295-5075,. 10.1209/0295-5075/79/60004
    • Baule, A. and Friedrich, R., " Two-point correlation function of the fractional Ornstein-Uhlenbeck process.," Europhys. Lett. 0295-5075 79, 60004 (2007). 10.1209/0295-5075/79/60004
    • (2007) Europhys. Lett. , vol.79 , pp. 60004
    • Baule, A.1    Friedrich, R.2
  • 4
    • 67650415773 scopus 로고    scopus 로고
    • E. Capelas de Oliveira (unpublished)
    • E. Capelas de Oliveira (unpublished).
  • 5
    • 67650415775 scopus 로고    scopus 로고
    • E. Capelas de Oliveira (unpublished)
    • E. Capelas de Oliveira (unpublished).
  • 7
    • 33746216416 scopus 로고    scopus 로고
    • Complex chemical kinetics in single enzyme molecules: Kramer's model with fractional Gaussian noise
    • 0021-9606,. 10.1063/1.2209231
    • Chaudhury, S. and Cherayil, B. J., " Complex chemical kinetics in single enzyme molecules: Kramer's model with fractional Gaussian noise.," J. Chem. Phys. 0021-9606 125, 024904 (2006). 10.1063/1.2209231
    • (2006) J. Chem. Phys. , vol.125 , pp. 024904
    • Chaudhury, S.1    Cherayil, B.J.2
  • 8
    • 41549101458 scopus 로고    scopus 로고
    • Differentiation to fractional orders and the fractional telegraph equation
    • 0022-2488,. 10.1063/1.2890375
    • Figueiredo Camargo, R., Chiacchio, A. O., and Capelas de Oliveira, E., " Differentiation to fractional orders and the fractional telegraph equation.," J. Math. Phys. 0022-2488 49, 033505 (2008). 10.1063/1.2890375
    • (2008) J. Math. Phys. , vol.49 , pp. 033505
    • Figueiredo Camargo, R.1    Chiacchio, A.O.2    Capelas De Oliveira, E.3
  • 9
    • 67650407745 scopus 로고    scopus 로고
    • WorkshoRobocontrol'08, Third Applied Robotic and Colaborative Systems Engineering, Unesp-Bauru, (unpublished).
    • Figueiredo Camargo, R., Capelas de Oliveira, E., and Vaz, J., Jr., Workshop Robocontrol'08, Third Applied Robotic and Colaborative Systems Engineering, Unesp-Bauru, 2008 (unpublished).
    • (2008)
    • Figueiredo Camargo, R.1    Capelas De Oliveira, E.2    Vaz Jr., J.3
  • 11
    • 33644764774 scopus 로고    scopus 로고
    • Anomalous diffusion in quantum Brownian motion with colored noise
    • 1050-2947,. 10.1103/PhysRevA.73.032103
    • Ford, G. W. and O'Connell, R. F., " Anomalous diffusion in quantum Brownian motion with colored noise.," Phys. Rev. A 1050-2947 73, 032103 (2006). 10.1103/PhysRevA.73.032103
    • (2006) Phys. Rev. A , vol.73 , pp. 032103
    • Ford, G.W.1    O'Connell, R.F.2
  • 12
    • 50849115153 scopus 로고    scopus 로고
    • Homogeneous Fractional embedding
    • 0022-2488,. 10.1063/1.2963497
    • Inizan, P., " Homogeneous Fractional embedding.," J. Math. Phys. 0022-2488 49, 082901 (2008). 10.1063/1.2963497
    • (2008) J. Math. Phys. , vol.49 , pp. 082901
    • Inizan, P.1
  • 14
    • 19744382497 scopus 로고    scopus 로고
    • Generalized Langevin equation with fractional Gaussian noise: Subdiffusion within a single protein molecule
    • 0031-9007,. 10.1103/PhysRevLett.93.180603
    • Kou, S. C. and Xie, X. S., " Generalized Langevin equation with fractional Gaussian noise: Subdiffusion within a single protein molecule.," Phys. Rev. Lett. 0031-9007 93, 180603 (2004). 10.1103/PhysRevLett.93.180603
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 180603
    • Kou, S.C.1    Xie, X.S.2
  • 15
    • 52349118652 scopus 로고    scopus 로고
    • Langevin equation with two fractional orders
    • 0375-9601,. 10.1016/j.physleta.2008.08.045
    • Lim, S. C., Li, M., and Teo, L. P., " Langevin equation with two fractional orders.," Phys. Lett. A 0375-9601 372, 6309 (2008). 10.1016/j.physleta.2008.08.045
    • (2008) Phys. Lett. A , vol.372 , pp. 6309
    • Lim, S.C.1    Li, M.2    Teo, L.P.3
  • 16
    • 0343368357 scopus 로고    scopus 로고
    • The fractional Langevin equation: Brownian motion revisited
    • 0213-8743.
    • Mainardi, F. and Pironi, P., " The fractional Langevin equation: Brownian motion revisited.," Extr. Math. 0213-8743 11, 140 (1996).
    • (1996) Extr. Math. , vol.11 , pp. 140
    • Mainardi, F.1    Pironi, P.2
  • 17
    • 0000393557 scopus 로고    scopus 로고
    • Nonlinear waves in reaction-diffusion systems: The effect of transport memory
    • 1063-651X,. 10.1103/PhysRevE.61.4177
    • Manne, K. K., Hurd, A. J., and Kenkre, V. M., " Nonlinear waves in reaction-diffusion systems: The effect of transport memory.," Phys. Rev. E 1063-651X 61, 4177 (2000). 10.1103/PhysRevE.61.4177
    • (2000) Phys. Rev. e , vol.61 , pp. 4177
    • Manne, K.K.1    Hurd, A.J.2    Kenkre, V.M.3
  • 18
    • 33845313674 scopus 로고    scopus 로고
    • A certain class of Laplace transform with applications to reaction and reaction-diffusion equations
    • 0004-640X,. 10.1007/s10509-006-9188-7
    • Mathai, A. M., Saxena, R. K., and Haubold, H. J., " A certain class of Laplace transform with applications to reaction and reaction-diffusion equations.," Astrophys. Space Sci. 0004-640X 305, 283 (2006). 10.1007/s10509-006-9188-7
    • (2006) Astrophys. Space Sci. , vol.305 , pp. 283
    • Mathai, A.M.1    Saxena, R.K.2    Haubold, H.J.3
  • 19
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guides to anomalous diffusion: A fractional kinetic equation
    • 0370-1573,. 10.1016/S0370-1573(00)00070-3
    • Metzler, R. and Klafter, J., " The random walk's guides to anomalous diffusion: A fractional kinetic equation.," Phys. Rep. 0370-1573 339, 1 (2000). 10.1016/S0370-1573(00)00070-3
    • (2000) Phys. Rep. , vol.339 , pp. 1
    • Metzler, R.1    Klafter, J.2
  • 20
    • 27144465458 scopus 로고    scopus 로고
    • Observation of a power-law memory kernel for fluctuations within a single protein molecule
    • 0031-9007,. 10.1103/PhysRevLett.94.198302
    • Min, W., Luo, G., Cherayil, B. J., Kou, S. C., and Xie, X. S., " Observation of a power-law memory kernel for fluctuations within a single protein molecule.," Phys. Rev. Lett. 0031-9007 94, 198302 (2005). 10.1103/PhysRevLett.94.198302
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 198302
    • Min, W.1    Luo, G.2    Cherayil, B.J.3    Kou, S.C.4    Xie, X.S.5
  • 21
    • 45849155458 scopus 로고    scopus 로고
    • Fractional Langevin model of memory in financial markets
    • 1063-651X,. 10.1103/PhysRevE.66.046118
    • Picozzi, S. and West, B. J., " Fractional Langevin model of memory in financial markets.," Phys. Rev. E 1063-651X 66, 046118 (2002). 10.1103/PhysRevE.66.046118
    • (2002) Phys. Rev. e , vol.66 , pp. 046118
    • Picozzi, S.1    West, B.J.2
  • 22
    • 0000222069 scopus 로고    scopus 로고
    • Generalized Langevin equations: Anomalous diffusion and probability distributions
    • 1063-651X,. 10.1103/PhysRevE.53.5872
    • Porr̀, J. M., Wang, K. G., and Masoliver, J., " Generalized Langevin equations: Anomalous diffusion and probability distributions.," Phys. Rev. E 1063-651X 53, 5872 (1996). 10.1103/PhysRevE.53.5872
    • (1996) Phys. Rev. e , vol.53 , pp. 5872
    • Porr̀, J.M.1    Wang, K.G.2    Masoliver, J.3
  • 23
    • 0842337110 scopus 로고
    • A singular integral equation with a generalized Mittag-Leffler function in the kernel
    • 0044-0523.
    • Prabhakar, T. R., " A singular integral equation with a generalized Mittag-Leffler function in the kernel.," Yokohama Math. J. 0044-0523 19, 7 (1971).
    • (1971) Yokohama Math. J. , vol.19 , pp. 7
    • Prabhakar, T.R.1
  • 24
    • 33745464287 scopus 로고    scopus 로고
    • Generalized Langevin equation with fractional derivative and long-time correlation function
    • 1063-651X,. 10.1103/PhysRevE.73.061104
    • Sau Fa, K., " Generalized Langevin equation with fractional derivative and long-time correlation function.," Phys. Rev. E 1063-651X 73, 061104 (2006). 10.1103/PhysRevE.73.061104
    • (2006) Phys. Rev. e , vol.73 , pp. 061104
    • Sau Fa, K.1
  • 25
    • 36749074902 scopus 로고    scopus 로고
    • Fractional Langevin equation and Riemann-Liouville fractional derivative
    • 1292-8941,. 10.1140/epje/i2007-10224-2
    • Sau Fa, K., " Fractional Langevin equation and Riemann-Liouville fractional derivative.," Eur. Phys. J. E 1292-8941 24, 139 (2007). 10.1140/epje/i2007-10224-2
    • (2007) Eur. Phys. J. e , vol.24 , pp. 139
    • Sau Fa, K.1
  • 26
    • 0034275979 scopus 로고    scopus 로고
    • Fractional calculus and continuous-time finance
    • 0378-4371,. 10.1016/S0378-4371(00)00255-7
    • Scalas, E., Gorenflo, R., and Mainardi, F., " Fractional calculus and continuous-time finance.," Physica A 0378-4371 284, 376 (2000). 10.1016/S0378-4371(00)00255-7
    • (2000) Physica A , vol.284 , pp. 376
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3
  • 27
    • 32844466709 scopus 로고    scopus 로고
    • Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle
    • 1063-651X,. 10.1103/PhysRevE.73.016111
    • Viales, A. D. and Despósito, M. A., " Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle.," Phys. Rev. E 1063-651X 73, 016111 (2006). 10.1103/PhysRevE.73. 016111
    • (2006) Phys. Rev. e , vol.73 , pp. 016111
    • Viales, A.D.1    Despósito, M.A.2
  • 28
    • 34147142844 scopus 로고    scopus 로고
    • Anomalous diffusion induced by a Mittag-Leffler correlated noise
    • 1063-651X,. 10.1103/PhysRevE.75.042102
    • Viales, A. D. and Despósito, M. A., " Anomalous diffusion induced by a Mittag-Leffler correlated noise.," Phys. Rev. E 1063-651X 75, 042102 (2007). 10.1103/PhysRevE.75.042102
    • (2007) Phys. Rev. e , vol.75 , pp. 042102
    • Viales, A.D.1    Despósito, M.A.2
  • 30
    • 33745194344 scopus 로고    scopus 로고
    • New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation
    • 0960-0779,. 10.1016/j.chaos.2005.08.151
    • Rui, Yu. and Zhang, H., " New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation.," Chaos, Solitons Fractals 0960-0779 30, 946 (2006). 10.1016/j.chaos.2005.08.151
    • (2006) Chaos, Solitons Fractals , vol.30 , pp. 946
    • Rui, Yu.1    Zhang, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.