-
3
-
-
10644269006
-
-
NASA's Glenn Research Center, Ohio
-
A. Freed, K. Diethelm, Y. Luchko, Fractional-order viscoelasticity (FOV): constitutive development using the fractional calculus, NASA's Glenn Research Center, Ohio, 2002.
-
(2002)
Fractional-order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus
-
-
Freed, A.1
Diethelm, K.2
Luchko, Y.3
-
4
-
-
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 1998 167 191
-
(1998)
Fract. Calc. Appl. Anal.
, vol.1
, pp. 167-191
-
-
Gorenflo, R.1
Mainardi, F.2
-
6
-
-
0030464353
-
Fractional relaxation-oscillation and fractional diffusion-wave phenomena
-
F. Mainardi Fractional relaxation-oscillation and fractional diffusion-wave phenomena Chaos Solitons Fractals 7 1996 1461 1477
-
(1996)
Chaos Solitons Fractals
, vol.7
, pp. 1461-1477
-
-
Mainardi, F.1
-
7
-
-
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
-
13
-
-
33751545053
-
Fractional high order methods for the nonlinear fractional ordinary differential equation
-
DOI 10.1016/j.na.2005.12.027, PII S0362546X05010503
-
R. Lin, and F. Liu Fractional high order methods for the nonlinear fractional ordinary differential equation Nonlinear Anal. 66 2007 856 869 (Pubitemid 44839109)
-
(2007)
Nonlinear Analysis, Theory, Methods and Applications
, vol.66
, Issue.4
, pp. 856-869
-
-
Lin, R.1
Liu, F.2
-
14
-
-
1542425102
-
Numerical solution of the space fractional Fokker-Planck equation
-
DOI 10.1016/j.cam.2003.09.028, PII S0377042703008616
-
F. Liu, V. Anh, and I. Turner Numerical solution of the space Fokker-Planck equation J. Comput. Appl. Math. 166 2004 209 219 (Pubitemid 38342127)
-
(2004)
Journal of Computational and Applied Mathematics
, vol.166
, Issue.1
, pp. 209-219
-
-
Liu, F.1
Anh, V.2
Turner, I.3
-
15
-
-
33751533397
-
Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation
-
(E)
-
F. Liu, S. Shen, V. Anh, and I. Turner Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation ANZIAM J. 46 2005 C488 C504 (E)
-
(2005)
ANZIAM J.
, vol.46
-
-
Liu, F.1
Shen, S.2
Anh, V.3
Turner, I.4
-
16
-
-
33846798041
-
Approximation of the Lévy-Feller advection-dispersion press by random walk and finite difference method
-
Q. Liu, F. Liu, I. Turner, and V. Anh Approximation of the Lévy-Feller advection-dispersion press by random walk and finite difference method J. Comput. Phys. 222 2007 57 70
-
(2007)
J. Comput. Phys.
, vol.222
, pp. 57-70
-
-
Liu, Q.1
Liu, F.2
Turner, I.3
Anh, V.4
-
17
-
-
34547673244
-
Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
-
DOI 10.1016/j.amc.2006.08.162, PII S0096300306012100
-
F. Liu, P. Zhuang, V. Anh, I. Turner, and K. Burrage Stability and convergence of difference methods for the space-time fractional advection-diffusion equation Appl. Math. Comput. 191 2007 12 20 (Pubitemid 47223382)
-
(2007)
Applied Mathematics and Computation
, vol.191
, Issue.1
, pp. 12-20
-
-
Liu, F.1
Zhuang, P.2
Anh, V.3
Turner, I.4
Burrage, K.5
-
18
-
-
4444368867
-
Finite difference approximations for fractional advection-dispersion flow equations
-
DOI 10.1016/j.cam.2004.01.033, PII S0377042704000986
-
M. Meerschaert, and C. Tadjeran Finite difference approximations for fractional advection-dispersion flow equation J. Comput. Appl. Math. 172 2004 65 77 (Pubitemid 39204390)
-
(2004)
Journal of Computational and Applied Mathematics
, vol.172
, Issue.1
, pp. 65-77
-
-
Meerschaert, M.M.1
Tadjeran, C.2
-
19
-
-
84867978055
-
Implicit difference approximation for the time fractional diffusion equation
-
Extra Edition
-
P. Zhang, and F. Liu Implicit difference approximation for the time fractional diffusion equation J. Appl. Math. Comput. 22 3 2006 87 99 (Pubitemid 44695544)
-
(2006)
Journal of Applied Mathematics and Computing
, vol.22
, Issue.3
, pp. 87-99
-
-
Zhuang, P.1
Liu, F.2
-
20
-
-
33646097441
-
Pattern formation in a fractional reaction diffusion system
-
V.V. Gafiychuk, and B.Yo. Datsko Pattern formation in a fractional reaction diffusion system Physica A 365 2006 300 306
-
(2006)
Physica A
, vol.365
, pp. 300-306
-
-
Gafiychuk, V.V.1
Datsko, B.Yo.2
-
22
-
-
0001983732
-
Fractional calculus: Some basic problems in continuum and statistical mechanics
-
A. Carpinteri, F. Mainardi, Springer New York
-
F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanics A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer New York 291 348
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
-
23
-
-
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 161 208
-
(2004)
J. Phys. A: Math. Gen.
, vol.37
, pp. 161-208
-
-
Metzler, R.1
Klafter, J.2
-
24
-
-
30244460855
-
The fundamental solutions for the fractional diffusion-wave equation
-
DOI 10.1016/0893-9659(96)00089-4, PII S0893965996000894
-
F. Mainardi The fundamental solutions for the fractional diffusion-wave equation Appl. Math. Lett. 9 1996 23 28 (Pubitemid 126365654)
-
(1996)
Applied Mathematics Letters
, vol.9
, Issue.6
, pp. 23-28
-
-
Mainardi, F.1
-
25
-
-
0001407424
-
The fundamental solution of the space-time fractional diffusion equation
-
F. Mainardi, Yu. Luchko, and G. Pagnini The fundamental solution of the space-time fractional diffusion equation Fract. Calc. Appl. Anal. 4 2 2001 153 192
-
(2001)
Fract. Calc. Appl. Anal.
, vol.4
, Issue.2
, pp. 153-192
-
-
Mainardi, F.1
Luchko, Yu.2
Pagnini, G.3
-
27
-
-
0009481303
-
The fractional diffusion equation
-
W. Wyss The fractional diffusion equation J. Math. Phys. 27 1986 2782 2785
-
(1986)
J. Math. Phys.
, vol.27
, pp. 2782-2785
-
-
Wyss, W.1
-
28
-
-
0001553919
-
Fractional diffusion and wave equations
-
W.R. Schneider, and W. Wyss Fractional diffusion and wave equations J. Math. Phys. 30 1989 134 144
-
(1989)
J. Math. Phys.
, vol.30
, pp. 134-144
-
-
Schneider, W.R.1
Wyss, W.2
-
29
-
-
0036650559
-
Solution for a fractional diffusion-wave equation defined in a bounded domain
-
DOI 10.1023/A:1016539022492, Fractional Order Calculus and Its Applications
-
O.P. Agrawal Solution for a fractional diffusion-wave equation defined in a bounded domain Nonlinear Dynam. 29 2002 145 155 (Pubitemid 34945396)
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 145-155
-
-
Agrawal, O.P.1
-
30
-
-
21144451936
-
Response of a diffusion-wave system subjected to deterministic and stochastic fields
-
O.P. Agrawal Response of a diffusion-wave system subjected to deterministic and stochastic fields ZAMM Z. Angew. Math. Mech. 83 2003 265 274
-
(2003)
ZAMM Z. Angew. Math. Mech.
, vol.83
, pp. 265-274
-
-
Agrawal, O.P.1
-
31
-
-
0040478884
-
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equation
-
R. Gorenflo, and F. Mainardi Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equation Matimyas Mat. 21 1998 109 118
-
(1998)
Matimyas Mat.
, vol.21
, pp. 109-118
-
-
Gorenflo, R.1
Mainardi, F.2
-
33
-
-
79952190735
-
Numerical method for solving diffusion-wave phenomena
-
M. Stojanovic Numerical method for solving diffusion-wave phenomena J. Comput. Appl. Math. 235 10 2011 3121 3137
-
(2011)
J. Comput. Appl. Math.
, vol.235
, Issue.10
, pp. 3121-3137
-
-
Stojanovic, M.1
-
34
-
-
0036339696
-
Time-domain modeling of constant-Q seismic waves using fractional derivatives
-
DOI 10.1007/s00024-002-8705-z, Seismic waves in laterally inhomogenous media
-
J.M. Carcione, F. Cavallini, F. Mainardi, and A. Hanyga Time-domain modeling of constant-Q seismic waves using fractional derivatives Pure Appl. Geophys. 159 2002 1719 1736 (Pubitemid 34861557)
-
(2002)
Pure and Applied Geophysics
, vol.159
, Issue.7-8
, pp. 1719-1736
-
-
Carcione, J.M.1
Cavallini, F.2
Mainardi, F.3
Hanyga, A.4
-
35
-
-
33846862055
-
Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
-
DOI 10.1016/j.ijsolstr.2006.07.008, PII S0020768306002757
-
Y.Z. Povstenko Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation Internat. J. Solids Structures 44 2007 2324 2348 (Pubitemid 46221404)
-
(2007)
International Journal of Solids and Structures
, vol.44
, Issue.7-8
, pp. 2324-2348
-
-
Povstenko, Y.Z.1
-
36
-
-
77949262762
-
Signaling problem for time-fractional diffusion-wave equation in a half-plane
-
Y.Z. Povstenko Signaling problem for time-fractional diffusion-wave equation in a half-plane Fract. Calc. Appl. Anal. 11 2008 329 352
-
(2008)
Fract. Calc. Appl. Anal.
, vol.11
, pp. 329-352
-
-
Povstenko, Y.Z.1
-
37
-
-
38349128567
-
Fundamental solution to three dimensional diffusion-wave equation and associated diffusive stresses
-
Y.Z. Povstenko Fundamental solution to three dimensional diffusion-wave equation and associated diffusive stresses Chaos Solitons Fractals 36 2008 961 972
-
(2008)
Chaos Solitons Fractals
, vol.36
, pp. 961-972
-
-
Povstenko, Y.Z.1
-
38
-
-
84862805797
-
Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates
-
Y.Z. Povstenko Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates Sci. Issues Jan. D Lugosz Univ. Czestochowa, Math. XIV 2009 97 104
-
(2009)
Sci. Issues Jan. D Lugosz Univ. Czestochowa, Math.
, vol.14
, pp. 97-104
-
-
Povstenko, Y.Z.1
-
39
-
-
77949274545
-
Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry
-
Y.Z. Povstenko Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry Nonlinear Dynam. 55 2010 593 605
-
(2010)
Nonlinear Dynam.
, vol.55
, pp. 593-605
-
-
Povstenko, Y.Z.1
-
40
-
-
67149125441
-
Time distributed order diffusion-wave equations. II. Applications of Laplace and Fouirer transformations
-
T.M. Atanackovic, S. Pilipovic, and D. Zorica Time distributed order diffusion-wave equations. II. Applications of Laplace and Fouirer transformations Proc. R. Soc. Lond. Ser. A 465 2009 1893 1917
-
(2009)
Proc. R. Soc. Lond. Ser. A
, vol.465
, pp. 1893-1917
-
-
Atanackovic, T.M.1
Pilipovic, S.2
Zorica, D.3
-
42
-
-
33845323067
-
Solution of generalized fractional reaction-diffusion equations
-
DOI 10.1007/s10509-006-9191-z
-
R.K. Saxena, A.M. Mathai, and H.J. Haubold Solution of generalized fractional reaction-diffusion equations Astrophys. Space Sci. 305 2006 305 313 (Pubitemid 44877998)
-
(2006)
Astrophysics and Space Science
, vol.305
, Issue.3
, pp. 305-313
-
-
Saxena, R.K.1
Mathai, A.M.2
Haubold, H.J.3
-
43
-
-
78449236821
-
Analytical solution for the time-fractional telegraph equation
-
doi:10.1155/2009/890158 Article ID 890158, 9 pages
-
F. Huang, Analytical solution for the time-fractional telegraph equation, J. Appl. Math. vol. 2009, Article ID 890158, 9 pages doi:10.1155/2009/890158.
-
J. Appl. Math.
, vol.2009
-
-
Huang, F.1
-
44
-
-
0742323831
-
Time-fractional telegraph equations and telegraph processes with brownian time
-
DOI 10.1007/s00440-003-0309-8
-
E. Orsingher, and L. Beghin Time-fractional telegraph equations and telegraph processes with Brownian time Probab. Theory Related Fields 128 1 2004 141 160 (Pubitemid 38157144)
-
(2004)
Probability Theory and Related Fields
, vol.128
, Issue.1
, pp. 141-160
-
-
Orsingher, E.1
Beghin, L.2
-
45
-
-
0035538580
-
Spectral analysis of fractional kinetic equations with random data
-
DOI 10.1023/A:1010474332598
-
V.V. Anh, and N.N. Leonenko Spectral analysis of fractional kinetic equations with random data J. Stat. Phys. 104 5-6 2001 1349 1387 (Pubitemid 33386576)
-
(2001)
Journal of Statistical Physics
, vol.104
, Issue.5-6
, pp. 1349-1387
-
-
Anh, V.V.1
Leonenko, N.N.2
-
46
-
-
84868213660
-
Solutions of unified fractional Schrodinger equations
-
Articale ID 935365, 7 pages
-
V.B.L. Chaurasia, and D. Kumar Solutions of unified fractional Schrodinger equations ISRN Math. Phys. 2012 Articale ID 935365, 7 pages
-
(2012)
ISRN Math. Phys.
-
-
Chaurasia, V.B.L.1
Kumar, D.2
-
47
-
-
0346897985
-
Mechanics with variable-order differential opearators
-
C.F.M. Coimdra Mechanics with variable-order differential opearators Ann. Phys. 12 2003 692 703
-
(2003)
Ann. Phys.
, vol.12
, pp. 692-703
-
-
Coimdra, C.F.M.1
-
48
-
-
67349184476
-
Some recent advances in theory and simulation of fractional diffusion processes
-
R. Gorenflo, and F. Mainardi Some recent advances in theory and simulation of fractional diffusion processes J. Comput. Appl. Math. 299 2009 400 415
-
(2009)
J. Comput. Appl. Math.
, vol.299
, pp. 400-415
-
-
Gorenflo, R.1
Mainardi, F.2
-
49
-
-
0036650957
-
Variable order and distributed order fractional operators
-
DOI 10.1023/A:1016586905654, Fractional Order Calculus and Its Applications
-
C.F. Lorenzo, and T.T. Hartley Variable order and distributed order fractional operators Nonlinear Dynam. 29 2002 57 98 (Pubitemid 34945393)
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 57-98
-
-
Lorenzo, C.F.1
Hartley, T.T.2
-
50
-
-
84868213661
-
Maximum principle for the fractional differential equations and its application
-
Badajoz, Spain, October 2010
-
Y. Luchko, Maximum principle for the fractional differential equations and its application, in: Proceedings of FDA'10, The 4th IFAC Workshop Fractional Differentiation and Applications, Badajoz, Spain, October 2010, pp. 18-22.
-
Proceedings of FDA'10, the 4th IFAC Workshop Fractional Differentiation and Applications
, pp. 18-22
-
-
Luchko, Y.1
-
51
-
-
77957822720
-
Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
-
Y. Luchko Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation J. Math. Anal. Appl. 374 2011 538 548
-
(2011)
J. Math. Anal. Appl.
, vol.374
, pp. 538-548
-
-
Luchko, Y.1
-
52
-
-
52349084738
-
Variable order modelling of diffusive-convective effects on the oscillatory flow past a sphere
-
H.T.C. Pedro, M.H. Kobayashi, J.M.C. Pereira, and C.F.M. Coimbra Variable order modelling of diffusive-convective effects on the oscillatory flow past a sphere J. Vib. Control 14 2008 1659 1672
-
(2008)
J. Vib. Control
, vol.14
, pp. 1659-1672
-
-
Pedro, H.T.C.1
Kobayashi, M.H.2
Pereira, J.M.C.3
Coimbra, C.F.M.4
-
53
-
-
56549085438
-
Maximum principle for the generalized time-fractional diffusion equation
-
Y. Luchko Maximum principle for the generalized time-fractional diffusion equation J. Math. Anal. Appl. 351 2009 218 223
-
(2009)
J. Math. Anal. Appl.
, vol.351
, pp. 218-223
-
-
Luchko, Y.1
-
54
-
-
34848822538
-
Analytical solution for the time-fractional telegraph equation by the method of separating variables
-
J. Chen, F. Liu, and V. Anh Analytical solution for the time-fractional telegraph equation by the method of separating variables J. Math. Anal. Appl. 338 2008 1364 1377
-
(2008)
J. Math. Anal. Appl.
, vol.338
, pp. 1364-1377
-
-
Chen, J.1
Liu, F.2
Anh, V.3
-
55
-
-
0004182307
-
-
Publ. House of Bulgarian Academy of Science Sofia
-
I.H. Dimovski Convolutional Calculus 1982 Publ. House of Bulgarian Academy of Science Sofia
-
(1982)
Convolutional Calculus
-
-
Dimovski, I.H.1
-
56
-
-
0012659515
-
An operational method for solving fractional differential equations with the Caputo derivatives
-
Y. Luchko, and R. Gorenflo An operational method for solving fractional differential equations with the Caputo derivatives Acta Math. Vietnam. 24 1999 207 233
-
(1999)
Acta Math. Vietnam.
, vol.24
, pp. 207-233
-
-
Luchko, Y.1
Gorenflo, R.2
-
58
-
-
44649089038
-
Boundary value problems for fractional diffusion-wave equation
-
V. Dafterdar-Gejji, and H. Jafari Boundary value problems for fractional diffusion-wave equation Aust. J. Math. Anal. Appl. 3 1 2006
-
(2006)
Aust. J. Math. Anal. Appl.
, vol.3
, Issue.1
-
-
Dafterdar-Gejji, V.1
Jafari, H.2
|