-
1
-
-
30244493399
-
Long memory processes and fractional integration in econometrics
-
Baillie R.T. Long memory processes and fractional integration in econometrics. J. Econom. 1996, 73:5-59.
-
(1996)
J. Econom.
, vol.73
, pp. 5-59
-
-
Baillie, R.T.1
-
2
-
-
84907996080
-
A new operational matrix of fractional integration for shifted Jacobi polynomials
-
in press
-
Bhrawy A.H., Tharwat M.M., Alghamdi M.A. A new operational matrix of fractional integration for shifted Jacobi polynomials. Bull. Malays. Math. Soc. 2014, in press.
-
(2014)
Bull. Malays. Math. Soc.
-
-
Bhrawy, A.H.1
Tharwat, M.M.2
Alghamdi, M.A.3
-
3
-
-
0003766476
-
-
Springer-Verlag, New York
-
Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A. Spectral Methods in Fluid Dynamics 1989, Springer-Verlag, New York.
-
(1989)
Spectral Methods in Fluid Dynamics
-
-
Canuto, C.1
Hussaini, M.Y.2
Quarteroni, A.3
Zang, T.A.4
-
4
-
-
84880635193
-
Sharp decay rates for wave equations with a fractional damping via new method in the Fourier space
-
Charo R.C., Luz C.R., Ikehata R. Sharp decay rates for wave equations with a fractional damping via new method in the Fourier space. J. Math. Anal. Appl. 2013, 408:247-255.
-
(2013)
J. Math. Anal. Appl.
, vol.408
, pp. 247-255
-
-
Charo, R.C.1
Luz, C.R.2
Ikehata, R.3
-
5
-
-
84867573206
-
The analytical solution and numerical solution of the fractional diffusion-wave equation with damping
-
Chen J., Liu F., Anh V., Shen S., Liu Q., Liao C. The analytical solution and numerical solution of the fractional diffusion-wave equation with damping. Appl. Math. Comput. 2012, 219:1737-1748.
-
(2012)
Appl. Math. Comput.
, vol.219
, pp. 1737-1748
-
-
Chen, J.1
Liu, F.2
Anh, V.3
Shen, S.4
Liu, Q.5
Liao, C.6
-
6
-
-
69049086472
-
Compact finite difference method for the fractional diffusion equation
-
Cui M.R. Compact finite difference method for the fractional diffusion equation. J. Comput. Phys. 2009, 228:7792-7804.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 7792-7804
-
-
Cui, M.R.1
-
7
-
-
84874394694
-
Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation
-
Cui M.R. Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation. Numer. Algorithms 2013, 62:383-409.
-
(2013)
Numer. Algorithms
, vol.62
, pp. 383-409
-
-
Cui, M.R.1
-
8
-
-
84899547717
-
Sumudu transform method for solving fractional differential equations and fractional diffusion-wave equation
-
Darzi R., Mohammadzade B., Mousavi S., Beheshti R. Sumudu transform method for solving fractional differential equations and fractional diffusion-wave equation. J. Math. Comput. Sci. 2013, 6:79-84.
-
(2013)
J. Math. Comput. Sci.
, vol.6
, pp. 79-84
-
-
Darzi, R.1
Mohammadzade, B.2
Mousavi, S.3
Beheshti, R.4
-
9
-
-
80052270048
-
A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
-
Doha E.H., Bhrawy A.H., Ezz-Eldien S.S. A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl. 2011, 62:2364-2373.
-
(2011)
Comput. Math. Appl.
, vol.62
, pp. 2364-2373
-
-
Doha, E.H.1
Bhrawy, A.H.2
Ezz-Eldien, S.S.3
-
10
-
-
84861893481
-
A new Jacobi operational matrix: an application for solving fractional differential equations
-
Doha E.H., Bhrawy A.H., Ezz-Eldien S.S. A new Jacobi operational matrix: an application for solving fractional differential equations. Appl. Math. Model. 2012, 36:4931-4943.
-
(2012)
Appl. Math. Model.
, vol.36
, pp. 4931-4943
-
-
Doha, E.H.1
Bhrawy, A.H.2
Ezz-Eldien, S.S.3
-
11
-
-
84890864220
-
Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method
-
Doha E.H., Bhrawy A.H., Ezz-Eldien S.S. Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method. Cent. Eur. J. Phys. 2013, 11:1494-1503.
-
(2013)
Cent. Eur. J. Phys.
, vol.11
, pp. 1494-1503
-
-
Doha, E.H.1
Bhrawy, A.H.2
Ezz-Eldien, S.S.3
-
12
-
-
77952888765
-
A compact difference scheme for the fractional diffusion-wave equation
-
Du R., Cao W.R., Sun Z.Z. A compact difference scheme for the fractional diffusion-wave equation. Appl. Math. Model. 2010, 34:2998-3007.
-
(2010)
Appl. Math. Model.
, vol.34
, pp. 2998-3007
-
-
Du, R.1
Cao, W.R.2
Sun, Z.Z.3
-
13
-
-
78649334165
-
A compact finite difference scheme for the fractional sub-diffusion equations
-
Gao G.H., Sun Z.Z. A compact finite difference scheme for the fractional sub-diffusion equations. J. Comput. Phys. 2011, 230:586-595.
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 586-595
-
-
Gao, G.H.1
Sun, Z.Z.2
-
14
-
-
84860213355
-
Extending the D'Alembert solution to space-time modified Riemann-Liouville fractional wave equations
-
Godinho C.F.L., Weberszpil J., Helayel-Neto J.A. Extending the D'Alembert solution to space-time modified Riemann-Liouville fractional wave equations. Chaos Solitons Fractals 2012, 45:765-771.
-
(2012)
Chaos Solitons Fractals
, vol.45
, pp. 765-771
-
-
Godinho, C.F.L.1
Weberszpil, J.2
Helayel-Neto, J.A.3
-
15
-
-
0007042083
-
Nonlinear oscillation with fractional derivative and its applications
-
He J.H. Nonlinear oscillation with fractional derivative and its applications. International Conference on Vibrating Engineering 1998, 288-291.
-
(1998)
International Conference on Vibrating Engineering
, pp. 288-291
-
-
He, J.H.1
-
16
-
-
0347763940
-
Some applications of nonlinear fractional differential equations and their applications
-
He J.H. Some applications of nonlinear fractional differential equations and their applications. Bull. Sci. Technol. 1999, 15(2):86-90.
-
(1999)
Bull. Sci. Technol.
, vol.15
, Issue.2
, pp. 86-90
-
-
He, J.H.1
-
17
-
-
79957810507
-
A compact finite difference scheme for the fourth-order fractional diffusion-wave system
-
Hu X., Zhang L. A compact finite difference scheme for the fourth-order fractional diffusion-wave system. Comput. Phys. Commun. 2011, 182:1645-1650.
-
(2011)
Comput. Phys. Commun.
, vol.182
, pp. 1645-1650
-
-
Hu, X.1
Zhang, L.2
-
18
-
-
83555172437
-
On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems
-
Hu X., Zhang L. On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems. Appl. Math. Comput. 2012, 218:5019-5034.
-
(2012)
Appl. Math. Comput.
, vol.218
, pp. 5019-5034
-
-
Hu, X.1
Zhang, L.2
-
19
-
-
35348938590
-
Solving fractional diffusion and wave equations by modified homotopy perturbation method
-
Jafari H., Momani S. Solving fractional diffusion and wave equations by modified homotopy perturbation method. Phys. Lett. A 2007, 370:388-396.
-
(2007)
Phys. Lett. A
, vol.370
, pp. 388-396
-
-
Jafari, H.1
Momani, S.2
-
20
-
-
84868196073
-
Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
-
Jiang H., Liu F., Turner I., Burrage K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Comput. Math. Appl. 2012, 64:3377-3388.
-
(2012)
Comput. Math. Appl.
, vol.64
, pp. 3377-3388
-
-
Jiang, H.1
Liu, F.2
Turner, I.3
Burrage, K.4
-
21
-
-
79952454978
-
Numerical approaches to fractional calculus and fractional ordinary differential equation
-
Li C.P., Chen A., Ye J.J. Numerical approaches to fractional calculus and fractional ordinary differential equation. J. Comput. Phys. 2011, 230:3352-3368.
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 3352-3368
-
-
Li, C.P.1
Chen, A.2
Ye, J.J.3
-
22
-
-
79960990048
-
Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
-
Li C.P., Zhao Z.G., Chen Y.Q. Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion. Comput. Math. Appl. 2011, 62:855-875.
-
(2011)
Comput. Math. Appl.
, vol.62
, pp. 855-875
-
-
Li, C.P.1
Zhao, Z.G.2
Chen, Y.Q.3
-
23
-
-
84871790575
-
Numerical methods for solving the multi-term time-fractional wave-diffusion equation
-
Liu F., Meerschaert M.M., McGough R.J., Zhuang P., Liu Q. Numerical methods for solving the multi-term time-fractional wave-diffusion equation. Fract. Calc. Appl. Anal. 2013, 16:9-25.
-
(2013)
Fract. Calc. Appl. Anal.
, vol.16
, pp. 9-25
-
-
Liu, F.1
Meerschaert, M.M.2
McGough, R.J.3
Zhuang, P.4
Liu, Q.5
-
25
-
-
3042776917
-
Fractional calculus in bioengineering
-
Magin R.L. Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 2004, 32(1):1-104.
-
(2004)
Crit. Rev. Biomed. Eng.
, vol.32
, Issue.1
, pp. 1-104
-
-
Magin, R.L.1
-
26
-
-
0001983732
-
Fractional calculus: 'Some basic problems in continuum and statistical mechanics'
-
Springer-Verlag, New York, A. Carpinteri, F. Mainardi (Eds.)
-
Mainardi F. Fractional calculus: 'Some basic problems in continuum and statistical mechanics'. Fractals and Fractional Calculus in Continuum Mechanics 1997, 291-348. Springer-Verlag, New York. A. Carpinteri, F. Mainardi (Eds.).
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
-
27
-
-
84926570205
-
Some noises with 1/f spectrum, a bridge between direct current and white noise
-
Mandelbrot B. Some noises with 1/f spectrum, a bridge between direct current and white noise. IEEE Trans. Inf. Theory 1967, 13(2):289-298.
-
(1967)
IEEE Trans. Inf. Theory
, vol.13
, Issue.2
, pp. 289-298
-
-
Mandelbrot, B.1
-
28
-
-
4043151477
-
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
-
Metzler R., Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 2004, 37:161-208.
-
(2004)
J. Phys. A
, vol.37
, pp. 161-208
-
-
Metzler, R.1
Klafter, J.2
-
29
-
-
34748865972
-
Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
-
Momani S., Odibat Z. Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations. Comput. Math. Appl. 2007, 54:910-919.
-
(2007)
Comput. Math. Appl.
, vol.54
, pp. 910-919
-
-
Momani, S.1
Odibat, Z.2
-
30
-
-
35349007529
-
Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
-
Momani S., Odibat Z., Erturk V.S. Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation. Phys. Lett. A 2007, 370:379-387.
-
(2007)
Phys. Lett. A
, vol.370
, pp. 379-387
-
-
Momani, S.1
Odibat, Z.2
Erturk, V.S.3
-
31
-
-
0021448875
-
To the theoretical explanation of the universal response
-
Nigmatullin R.R. To the theoretical explanation of the universal response. Phys. Status Solidi, B Basic Res. 1984, 123(2):739-745.
-
(1984)
Phys. Status Solidi, B Basic Res.
, vol.123
, Issue.2
, pp. 739-745
-
-
Nigmatullin, R.R.1
-
32
-
-
0022492943
-
Realization of the generalized transfer equation in a medium with fractal geometry
-
Nigmatullin R.R. Realization of the generalized transfer equation in a medium with fractal geometry. Phys. Status Solidi, B Basic Res. 1986, 133(1):425-430.
-
(1986)
Phys. Status Solidi, B Basic Res.
, vol.133
, Issue.1
, pp. 425-430
-
-
Nigmatullin, R.R.1
-
34
-
-
84884805515
-
An efficient Chebyshev-tau method for solving the space fractional diffusion equations
-
Ren R., Li H., Jiang W., Song M. An efficient Chebyshev-tau method for solving the space fractional diffusion equations. Appl. Math. Comput. 2013, 224:259-267.
-
(2013)
Appl. Math. Comput.
, vol.224
, pp. 259-267
-
-
Ren, R.1
Li, H.2
Jiang, W.3
Song, M.4
-
35
-
-
84868502319
-
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
-
Ren J., Sun Z.-Z., Zhao X. Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions. J. Comput. Phys. 2013, 232:456-467.
-
(2013)
J. Comput. Phys.
, vol.232
, pp. 456-467
-
-
Ren, J.1
Sun, Z.-Z.2
Zhao, X.3
-
36
-
-
0030867045
-
Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
-
Rossikhin Y.A., Shitikova M.V. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 1997, 50:15-67.
-
(1997)
Appl. Mech. Rev.
, vol.50
, pp. 15-67
-
-
Rossikhin, Y.A.1
Shitikova, M.V.2
-
37
-
-
79960977916
-
A tau approach for solution of the space fractional diffusion equation
-
Saadatmandi A., Dehghan M. A tau approach for solution of the space fractional diffusion equation. Comput. Math. Appl. 2011, 62:1135-1142.
-
(2011)
Comput. Math. Appl.
, vol.62
, pp. 1135-1142
-
-
Saadatmandi, A.1
Dehghan, M.2
-
38
-
-
84886296093
-
Stable multi-domain spectral penalty methods for fractional partial differential equations
-
Xu Q., Hesthaven J.S. Stable multi-domain spectral penalty methods for fractional partial differential equations. J. Comput. Phys. 2014, 257:241-258.
-
(2014)
J. Comput. Phys.
, vol.257
, pp. 241-258
-
-
Xu, Q.1
Hesthaven, J.S.2
-
39
-
-
84886791142
-
Exponentially accurate spectral and spectral element methods for fractional ODEs
-
Zayernouri M., Karniadakis G.E. Exponentially accurate spectral and spectral element methods for fractional ODEs. J. Comput. Phys. 2014, 257:460-480.
-
(2014)
J. Comput. Phys.
, vol.257
, pp. 460-480
-
-
Zayernouri, M.1
Karniadakis, G.E.2
-
40
-
-
84892586026
-
The use of finite difference/element approaches for solving the time-fractional subdiffusion equation
-
Zeng F., Li C., Liu F., Turner I. The use of finite difference/element approaches for solving the time-fractional subdiffusion equation. SIAM J. Sci. Comput. 2013, 35(6):A2976-A3000.
-
(2013)
SIAM J. Sci. Comput.
, vol.35
, Issue.6
, pp. A2976-A3000
-
-
Zeng, F.1
Li, C.2
Liu, F.3
Turner, I.4
|