-
1
-
-
27244435100
-
Harmonic velocity noise: Non-markovian features of noise-driven systems at long times
-
J.-D. Bao, Y.-L. Song, Q. Ji and Y.-Z. Zhuo, Harmonic velocity noise: non-Markovian features of noise-driven systems at long times. Phys. Rev. E 72 (2005), 011113/1-7.
-
(2005)
Phys. Rev. E
, vol.72
, pp. 0111131-0111137
-
-
Bao, J.-D.1
Song, Y.-L.2
Ji, Q.3
Zhuo, Y.-Z.4
-
2
-
-
51849083802
-
Fractional langevin equation: Overdamped, underdamped, and critical behaviors
-
031112
-
S. Burov and E. Barkai, Fractional Langevin equation: Overdamped, underdamped, and critical behaviors. Phys. Rev. E 78 (2008), 031112/1-18.
-
(2008)
Phys. Rev. E
, vol.78
, pp. 1-18
-
-
Burov, S.1
Barkai, E.2
-
3
-
-
78751668316
-
Single particle tracking in systems showing anomalous diffusion: The role of weak ergodicity breaking
-
S. Burov, J.-H. Jeon, R. Metzler and E. Barkai, Single particle tracking in systems showing anomalous diffusion: The role of weak ergodicity breaking. Phys. Chem. Chem. Phys. 13 (2011), 1800-1812.
-
(2011)
Phys. Chem. Chem. Phys.
, vol.13
, pp. 1800-1812
-
-
Burov, S.1
Jeon, J.-H.2
Metzler, R.3
Barkai, E.4
-
4
-
-
77955785256
-
Aging and nonergodicity beyond the khinchin theorem
-
S. Burov, R. Metzler and E. Barkai, Aging and nonergodicity beyond the Khinchin theorem. Proc. Natl. Acad. Sci. USA 107 (2010), 13228-13233.
-
(2010)
Proc. Natl. Acad. Sci. USA
, vol.107
, pp. 13228-13233
-
-
Burov, S.1
Metzler, R.2
Barkai, E.3
-
5
-
-
67650479716
-
Solution of the fractional langevin equation and the mittag-leffler functions
-
063507
-
R.F. Camargo, A.O. Chiacchio, R. Charnet and E. Capelas de Oliveira, Solution of the fractional Langevin equation and the Mittag-Leffler functions. J. Math. Phys. 50 (2009), 063507/1-8.
-
(2009)
J. Math. Phys.
, vol.50
, pp. 1-8
-
-
Camargo, R.F.1
Chiacchio, A.O.2
Charnet, R.3
Capelas De Oliveira, E.4
-
6
-
-
73949134592
-
On anomalous diffusion and the fractional generalized langevin equation for a harmonic oscillator
-
123518
-
R.F. Camargo, E. Capelas de Oliveira and J. Vaz Jr, On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator. J. Math. Phys. 50 (2009), 123518/1-13.
-
(2009)
J. Math. Phys.
, vol.50
, pp. 1-13
-
-
Camargo, R.F.1
Capelas De Oliveira, E.2
Vaz Jr., J.3
-
7
-
-
79953685491
-
Models based on mittag-leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J
-
E. Capelas de Oliveira, F. Mainardi and J. Vaz Jr., Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J., Special Topics 193 (2011), 161-171.
-
(2011)
Special Topics
, vol.193
, pp. 161-171
-
-
Capelas De Oliveira, E.1
Mainardi, F.2
Vaz Jr., J.3
-
9
-
-
59349102367
-
Ergodic properties of fractional brownian-langevin motion
-
011112
-
W. Deng and E. Barkai, Ergodic properties of fractional Brownian-Langevin motion. Phys. Rev. E 79 (2009), 011112/1-7.
-
(2009)
Phys. Rev. E
, vol.79
, pp. 1-7
-
-
Deng, W.1
Barkai, E.2
-
10
-
-
69449105795
-
Subdiffusive behavior in a trapping potential: Mean square displacement and velocity autocorrelation function
-
021111
-
M.A. Desṕosito and A.D. Vinales, Subdiffusive behavior in a trapping potential: Mean square displacement and velocity autocorrelation function. Phys. Rev. E 80 (2009), 021111/1-7.
-
(2009)
Phys. Rev. E
, vol.80
, pp. 1-7
-
-
Desṕosito, M.A.1
Vinales, A.D.2
-
11
-
-
78751563119
-
Fractional brownian motion approach to polymer translocation: The governing equation of motion
-
011802/
-
J.L.A. Dubbeldam, V.G. Rostiashvili, A. Milchev and T.A. Vilgis, Fractional Brownian motion approach to polymer translocation: The governing equation of motion. Phys. Rev. E 83 (2011), 011802/1-8.
-
(2011)
Phys. Rev. E
, vol.83
, pp. 1-8
-
-
Dubbeldam, J.L.A.1
Rostiashvili, V.G.2
Milchev, A.3
Vilgis, T.A.4
-
12
-
-
77951086281
-
Fractional generalized langevin equation approach to single-file diffusion
-
C.H. Eab and S.C. Lim, Fractional generalized Langevin equation approach to single-file diffusion. Physica A 389 (2010) 2510-2521.
-
(2010)
Physica A
, vol.389
, pp. 2510-2521
-
-
Eab, C.H.1
Lim, S.C.2
-
13
-
-
79961097638
-
Fractional langevin equations of distributed order
-
031136/
-
C.H. Eab and S.C. Lim, Fractional Langevin equations of distributed order. Phys. Rev. E 83 (2011), 031136/1-10.
-
(2011)
Phys. Rev. E
, vol.83
, pp. 1-10
-
-
Eab, C.H.1
Lim, S.C.2
-
14
-
-
84858979441
-
Accelerating and retarding anomalous diffusion
-
145001/
-
C.H. Eab and S.C. Lim, Accelerating and retarding anomalous diffusion. J. Phys. A: Math. Theor. 45 (2012), 145001/1-17.
-
(2012)
J. Phys. A: Math. Theor.
, vol.45
, pp. 1-17
-
-
Eab, C.H.1
Lim, S.C.2
-
15
-
-
33745464287
-
Generalized langevin equation with fractional derivative and long-time correlation function
-
061104
-
K.S. Fa, Generalized Langevin equation with fractional derivative and long-time correlation function. Phys. Rev. E 73 (2006), 061104/1-4.
-
(2006)
Phys. Rev. E
, vol.73
, pp. 1-4
-
-
Fa, K.S.1
-
16
-
-
84869182788
-
Continuous-time random walk: Exact solutions for the probability density function and first two moments
-
045022
-
K.S. Fa and J. Fat, Continuous-time random walk: exact solutions for the probability density function and first two moments. Phys. Scr. 84 (2011), 045022/1-6.
-
(2011)
Phys. Scr.
, vol.84
, pp. 1-6
-
-
Fa, K.S.1
Fat, J.2
-
17
-
-
33644885029
-
Physical nature of bacterial cytoplasm
-
098102
-
I. Golding and E.C. Cox, Physical nature of bacterial cytoplasm. Phys. Rev. Lett. 96 (2006), 098102/1-4.
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 1-4
-
-
Golding, I.1
Cox, E.C.2
-
18
-
-
0000361678
-
Random walk models for space-fractional diffusion processes
-
R. Gorenflo and F. Mainardi, Random walk models for Space-Fractional Diffusion Processes. Fract. Calc. Appl. Anal. 1, No 2 (1998), 167-192; http://www.math.bas.bg/fcaa
-
(1998)
Fract. Calc. Appl. Anal.
, vol.1
, Issue.2
, pp. 167-192
-
-
Gorenflo, R.1
Mainardi, F.2
-
19
-
-
33646113530
-
Simply and multiply scaled diffusion limits for continuous time random walks
-
R. Gorenflo and F. Mainardi, Simply and multiply scaled diffusion limits for continuous time random walks. Journal of Physics: Conference Series 7 (2005), 1-16.
-
(2005)
Journal of Physics: Conference Series
, vol.7
, pp. 1-16
-
-
Gorenflo, R.1
Mainardi, F.2
-
20
-
-
70449103071
-
Viscoelastic subdiffusion: From anomalous to normal
-
046125
-
I. Goychuk, Viscoelastic subdiffusion: From anomalous to normal. Phys. Rev. E 80 (2009), 046125/1-11.
-
(2009)
Phys. Rev. E
, vol.80
, pp. 1-11
-
-
Goychuk, I.1
-
21
-
-
48849092363
-
Random time-scale invariant diffusion and transport coefficients
-
058101
-
Y. He, S. Burov, R. Metzler and E. Barkai, Random time-scale invariant diffusion and transport coefficients. Phys. Rev. Lett. 101 (2008), 058101/1-4.
-
(2008)
Phys. Rev. Lett.
, vol.101
, pp. 1-4
-
-
He, Y.1
Burov, S.2
Metzler, R.3
Barkai, E.4
-
23
-
-
0141955949
-
On fractional diffusion and continuous time random walks
-
R. Hilfer, On fractional diffusion and continuous time random walks. Physica A 329 (2003), 35-40.
-
(2003)
Physica A
, vol.329
, pp. 35-40
-
-
Hilfer, R.1
-
24
-
-
76649121192
-
Fractional brownian motion and motion governed by the fractional langevin equation in confined geometries
-
021103/
-
J.-H. Jeon and R. Metzler, Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries. Phys. Rev. E 81 (2010), 021103/1-11.
-
(2010)
Phys. Rev. E
, vol.81
, pp. 1-11
-
-
Jeon, J.-H.1
Metzler, R.2
-
25
-
-
79251477200
-
In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
-
048103
-
J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sorensen, L. Oddershede and R. Metzler, In vivo anomalous diffusion and weak ergodicity breaking of lipid granules. Phys. Rev. Lett. 106 (2011), 048103/1-4; http://arxiv.org/abs/1010.0347
-
(2011)
Phys. Rev. Lett.
, vol.106
, pp. 1-4
-
-
Jeon, J.-H.1
Tejedor, V.2
Burov, S.3
Barkai, E.4
Selhuber-Unkel, C.5
Berg-Sorensen, K.6
Oddershede, L.7
Metzler, R.8
-
26
-
-
19744382497
-
Generalized langevin equation with fractional gaussian noise: Subdiffusion within a single protein molecule
-
180603
-
S.C. Kou and X.S. Xie, Generalized Langevin equation with fractional Gaussian noise: Subdiffusion within a single protein molecule. Phys. Rev. Lett. 93 (2004), 180603/1-4.
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 1-4
-
-
Kou, S.C.1
Xie, X.S.2
-
27
-
-
33847327575
-
The fluctuation-dissipation theorem
-
R. Kubo, The fluctuation-dissipation theorem. Rep. Prog. Phys. 29 (1966), 255-284.
-
(1966)
Rep. Prog. Phys.
, vol.29
, pp. 255-284
-
-
Kubo, R.1
-
28
-
-
70449409239
-
Modeling single-file diffusion with step fractional brownian motion and a generalized fractional langevin equation
-
S.C. Lim and L.P. Teo, Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation. J. Stat. Mech. P08015 (2009).
-
(2009)
J. Stat. Mech.
-
-
Lim, S.C.1
Teo, L.P.2
-
29
-
-
0035509430
-
Fractional langevin equation
-
051106
-
E. Lutz, Fractional Langevin equation. Phys. Rev. E 64 (2001), 051106/1-4.
-
(2001)
Phys. Rev. E
, vol.64
, pp. 1-4
-
-
Lutz, E.1
-
30
-
-
0343368357
-
The fractional langevin equation: Brownian motion revisited
-
F. Mainardi and P. Pironi, The fractional Langevin equation: Brownian motion revisited. Extr. Math. 11 (1996), 140-154.
-
(1996)
Extr. Math.
, vol.11
, pp. 140-154
-
-
Mainardi, F.1
Pironi, P.2
-
31
-
-
0001983732
-
Some basic problems in continuum and statistical mechanics
-
In: A. Carpinteri and F. Mainardi (Eds.) Springer-Verlag, Wien and New York
-
F. Mainardi, Fractional Calculus: Some basic problems in continuum and statistical mechanics. In: A. Carpinteri and F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien and New York (1997), 291-348.
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
Calculus, F.2
-
32
-
-
0001825293
-
A dynamical approach to fractional brownian motion
-
R. Mannella, P. Grigolini and B.J. West, A dynamical approach to fractional Brownian motion. Fractals 2 (1994), 81-94.
-
(1994)
Fractals
, vol.2
, pp. 81-94
-
-
Mannella, R.1
Grigolini, P.2
West, B.J.3
-
33
-
-
0034318338
-
Generalized chapman-kolmogorov equation: A unifying approach to the description of anomalous transport in external fields
-
R. Metzler, Generalized Chapman-Kolmogorov equation: A unifying approach to the description of anomalous transport in external fields. Phys. Rev. E 62 (2000), 6233-6245.
-
(2000)
Phys. Rev. E
, vol.62
, pp. 6233-6245
-
-
Metzler, R.1
-
34
-
-
18144408075
-
Anomalous diffusion and relaxation close to thermal equilibrium: A fractional fokker-planck equation approach
-
R. Metzler, E. Barkai and J. Klafter, Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82 (1999), 3563-3567.
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 3563-3567
-
-
Metzler, R.1
Barkai, E.2
Klafter, J.3
-
35
-
-
0002641421
-
The random walk's guide to anomalous diffusion: A fractional dynamics approach
-
R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000), 1-77.
-
(2000)
Phys. Rep.
, vol.339
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
36
-
-
0141642079
-
When translocation dynamics becomes anomalous
-
R. Metzler and J. Klafter, When translocation dynamics becomes anomalous. Biophys. J. 85 (2003), 2776-2779.
-
(2003)
Biophys. J.
, vol.85
, pp. 2776-2779
-
-
Metzler, R.1
Klafter, J.2
-
37
-
-
4043151477
-
The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
-
R. Metzler and J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A: Math. Gen. 37 (2004), R161-R208.
-
(2004)
J. Phys. A: Math. Gen.
, vol.37
-
-
Metzler, R.1
Klafter, J.2
-
39
-
-
0037437756
-
Aging properties of an anomalously diffusing particule
-
N. Pottier, Aging properties of an anomalously diffusing particule. Physica A 317 (2003), 371-382.
-
(2003)
Physica A
, vol.317
, pp. 371-382
-
-
Pottier, N.1
-
40
-
-
0842337110
-
A singular integral equation with a generalized mittag-leffler function in the kernel
-
T.R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama Math. J. 19 (1971), 7-15.
-
(1971)
Yokohama Math. J.
, vol.19
, pp. 7-15
-
-
Prabhakar, T.R.1
-
41
-
-
79957862593
-
Fractional diffusion equation with a generalized riemann-liouville time fractional derivative
-
255203
-
T. Sandev, R. Metzler and Z . Tomovski, Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative. J. Phys. A: Math. Theor. 44 (2011), 255203/1-21.
-
(2011)
J. Phys. A: Math. Theor.
, vol.44
, pp. 1-21
-
-
Sandev, T.1
Metzler, R.2
Tomovski, Z.3
-
42
-
-
78149375676
-
Asymptotic behavior of a harmonic oscillator driven by a generalized mittag-leffler noise
-
065001
-
T. Sandev and Z. Tomovski, Asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise. Phys. Scr. 82 (2010), 065001/1-4.
-
(2010)
Phys. Scr.
, vol.82
, pp. 1-4
-
-
Sandev, T.1
Tomovski, Z.2
-
43
-
-
80054890030
-
Generalized langevin equation with a three parameter mittag-leffler noise
-
T. Sandev, Z. Tomovski and J.L.A. Dubbeldam, Generalized Langevin equation with a three parameter Mittag-Leffler noise. Physica A 390 (2011), 3627-3636.
-
(2011)
Physica A
, vol.390
, pp. 3627-3636
-
-
Sandev, T.1
Tomovski, Z.2
Dubbeldam, J.L.A.3
-
44
-
-
3142703861
-
Unified fractional kinetic equation and a fractional diffusion equation
-
R.K. Saxena, A.M. Mathai and H.J. Haubold, Unified fractional kinetic equation and a fractional diffusion equation. Astrophysics and Space Sciences 209 (2004), 299-310.
-
(2004)
Astrophysics and Space Sciences
, vol.209
, pp. 299-310
-
-
Saxena, R.K.1
Mathai, A.M.2
Haubold, H.J.3
-
45
-
-
51249114478
-
Certain properties of fractional calculus operators associated with generalized mittag-leffler function
-
available at
-
R.K. Saxena and M. Saigo, Certain properties of fractional calculus operators associated with generalized Mittag-Leffler function. Fract. Calc. Appl. Anal. 8, No 2 (2005), 141-154; available at http://www.math.bas.bg/fcaa/ volume8/fcaa82/saxena saigo 82.pdf.
-
(2005)
Fract. Calc. Appl. Anal.
, vol.8
, Issue.2
, pp. 141-154
-
-
Saxena, R.K.1
Saigo, M.2
-
46
-
-
0141508296
-
Anomalous transit-time dispersion in amorphous solids
-
H. Scher H and E.W. Montroll, Anomalous transit-time dispersion in amorphous solids. Phys. Rev. B 12 (1975), 2455-2477.
-
(1975)
Phys. Rev. B
, vol.12
, pp. 2455-2477
-
-
H. Scher, H.1
Montroll, E.W.2
-
47
-
-
77951596339
-
Kramers-like escape driven by fractional gaussian noise
-
041119/
-
O.Y. Sliusarenko, V.Y. Gonchar, A.V. Chechkin, I.M. Sokolov, and R. Metzler, Kramers-like escape driven by fractional Gaussian noise. Phys. Rev. E 81 (2010), 041119/1-14.
-
(2010)
Phys. Rev. E
, vol.81
, pp. 1-14
-
-
Sliusarenko, O.Y.1
Gonchar, V.Y.2
Chechkin, A.V.3
Sokolov, I.M.4
Metzler, R.5
-
48
-
-
64449085065
-
Fractional calculus with an integral operator containing a generalized mittag-leffler function in the kernel
-
H.M. Srivastava and Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel. Appl. Math. Comput. 211 (2009), 198-210.
-
(2009)
Appl. Math. Comput.
, vol.211
, pp. 198-210
-
-
Srivastava, H.M.1
Tomovski, Z.2
-
49
-
-
81455131424
-
Numerical scheme for calculating of the fractional two-power relaxation laws in time-domain of measurements
-
A. Stanislavsky and K. Weron, Numerical scheme for calculating of the fractional two-power relaxation laws in time-domain of measurements. Computer Physics Communications 183 (2012), 320-323.
-
(2012)
Computer Physics Communications
, vol.183
, pp. 320-323
-
-
Stanislavsky, A.1
Weron, K.2
-
50
-
-
27144559157
-
Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles
-
107401
-
J. Tang J and R.A. Marcus, Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles. Phys. Rev. Lett. 95 (2005), 107401/1-4.
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 1-4
-
-
J. Tang, J.1
Marcus, R.A.2
-
51
-
-
78049494452
-
Fractional and operational calculus with generalized fractional derivative operators and mittag-leffler type functions
-
Z. Tomovski, R. Hilfer and H.M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions. Integral Transform. Spec. Func. 21 (2010), 797-814.
-
(2010)
Integral Transform. Spec. Func.
, vol.21
, pp. 797-814
-
-
Tomovski, Z.1
Hilfer, R.2
Srivastava, H.M.3
-
52
-
-
84856954497
-
Generalized space-time fractional diffusion equation with composite fractional time derivative
-
Z. Tomovski, T. Sandev, R. Metzler and J. Dubbeldam, Generalized space-time fractional diffusion equation with composite fractional time derivative. Physica A 391 (2012), 2527-2542.
-
(2012)
Physica A
, vol.391
, pp. 2527-2542
-
-
Tomovski, Z.1
Sandev, T.2
Metzler, R.3
Dubbeldam, J.4
-
53
-
-
32844466709
-
Anomalous diffusion: Exact solution of the generalized langevin equation for harmonically bounded particle
-
016111
-
A.D. Vinales andM.A. Desṕosito, Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle. Phys. Rev. E 73 (2006), 016111/1-4.
-
(2006)
Phys. Rev. E
, vol.73
, pp. 1-4
-
-
Vinales, A.D.1
Desṕosito, M.A.2
-
54
-
-
34147142844
-
Anomalous diffusion induced by a mittag-leffler correlated noise
-
042102
-
A.D. Vinales and M.A. Desṕosito, Anomalous diffusion induced by a Mittag-Leffler correlated noise. Phys. Rev. E 75 (2007), 042102/1-4.
-
(2007)
Phys. Rev. E
, vol.75
, pp. 1-4
-
-
Vinales, A.D.1
Desṕosito, M.A.2
-
55
-
-
68849086867
-
Anomalous diffusive behavior of a harmonic oscillator driven by a mittag-leffler noise
-
011101/1-6
-
A.D. Vinales, K.G. Wang and M.A. Desṕosito, Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise. Phys. Rev. E 80 (2009), 011101/1-6.
-
(2009)
Phys. Rev. E
, vol.80
-
-
Vinales, A.D.1
Wang, K.G.2
Desṕosito, M.A.3
-
56
-
-
0032625656
-
Nonequilibrium statistical description of anomalous diffusion
-
K.G. Wang and M. Tokuyama, Nonequilibrium statistical description of anomalous diffusion. Physica A 265 (1999), 341-351.
-
(1999)
Physica A
, vol.265
, pp. 341-351
-
-
Wang, K.G.1
Tokuyama, M.2
-
57
-
-
77953494844
-
Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm
-
238102/
-
S.C. Weber, A.J. Spakowitz and J.A. Theriot, Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm. Phys. Rev. Lett. 104 (2010), 238102/1-4.
-
(2010)
Phys. Rev. Lett.
, vol.104
, pp. 1-4
-
-
Weber, S.C.1
Spakowitz, A.J.2
Theriot, J.A.3
|