-
2
-
-
0003593401
-
-
Academic Press, Inc, New York, London
-
Oldham K.B., Spanier J. Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order 1974, Academic Press, Inc, New York, London.
-
(1974)
Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order
-
-
Oldham, K.B.1
Spanier, J.2
-
4
-
-
77957308442
-
A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation
-
Amairi M., Aoun M., Najar S., Abdelkrim M.N. A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation. Appl. Math. Comput. 2010, 217:2162-2168.
-
(2010)
Appl. Math. Comput.
, vol.217
, pp. 2162-2168
-
-
Amairi, M.1
Aoun, M.2
Najar, S.3
Abdelkrim, M.N.4
-
5
-
-
77950188013
-
Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
-
Deng J., Ma L. Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. Appl. Math. Lett. 2010, 23:676-680.
-
(2010)
Appl. Math. Lett.
, vol.23
, pp. 676-680
-
-
Deng, J.1
Ma, L.2
-
6
-
-
79955481320
-
A sufficient condition of viability for fractional differential equations with the Caputo derivative
-
Girejko E., Mozyrska D., Wyrwas M. A sufficient condition of viability for fractional differential equations with the Caputo derivative. J. Math. Anal. Appl. 2011, 382(1):146-154.
-
(2011)
J. Math. Anal. Appl.
, vol.382
, Issue.1
, pp. 146-154
-
-
Girejko, E.1
Mozyrska, D.2
Wyrwas, M.3
-
7
-
-
17444386836
-
Solution of an extraordinary differential equation by adomian decomposition method
-
Ray S.S., Bera R.K. Solution of an extraordinary differential equation by adomian decomposition method. J. Appl. Math. 2004, 4:331-338.
-
(2004)
J. Appl. Math.
, vol.4
, pp. 331-338
-
-
Ray, S.S.1
Bera, R.K.2
-
8
-
-
76649094637
-
Solving nonlinear fractional partial differential equations using the homotopy analysis method
-
Dehghan M., Manafian J., Saadatmandi A. Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer. Methods Partial Diff. Eq. 2010, 26:448-479.
-
(2010)
Numer. Methods Partial Diff. Eq.
, vol.26
, pp. 448-479
-
-
Dehghan, M.1
Manafian, J.2
Saadatmandi, A.3
-
10
-
-
70350378693
-
A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
-
Odibat Z., Momani S., Xu H. A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations. Appl. Math. Model. 2010, 34:593-600.
-
(2010)
Appl. Math. Model.
, vol.34
, pp. 593-600
-
-
Odibat, Z.1
Momani, S.2
Xu, H.3
-
11
-
-
78049255335
-
Convergence of the variational iteration method for solving multi-order fractional differential equations
-
Yang S., Xiao A., Su H. Convergence of the variational iteration method for solving multi-order fractional differential equations. Comput. Math. Appl. 2010, 60:2871-2879.
-
(2010)
Comput. Math. Appl.
, vol.60
, pp. 2871-2879
-
-
Yang, S.1
Xiao, A.2
Su, H.3
-
12
-
-
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
-
13
-
-
74249095517
-
A new operational matrix for solving fractional-order differential equations
-
Saadatmandi A., Dehghan M. A new operational matrix for solving fractional-order differential equations. Comput. Math. Appl. 2010, 59:1326-1336.
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1326-1336
-
-
Saadatmandi, A.1
Dehghan, M.2
-
14
-
-
79960555480
-
Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
-
Doha E.H., Bhrawy A.H., Ezz-Eldien S.S. Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Appl. Math. Model. 2011, 35:5662-5672.
-
(2011)
Appl. Math. Model.
, vol.35
, pp. 5662-5672
-
-
Doha, E.H.1
Bhrawy, A.H.2
Ezz-Eldien, S.S.3
-
15
-
-
79961168894
-
A quadrature tau method for variable coefficients fractional differential equations
-
Bhrawy A.H., Alofi A.S., Ezz-Eldien S.S. A quadrature tau method for variable coefficients fractional differential equations. Appl. Math. Lett. 2011, 24:2146-2152.
-
(2011)
Appl. Math. Lett.
, vol.24
, pp. 2146-2152
-
-
Bhrawy, A.H.1
Alofi, A.S.2
Ezz-Eldien, S.S.3
-
16
-
-
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
-
17
-
-
78649445937
-
An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis
-
Ghoreishi F., Yazdani S. An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis. Comput. Math. Appl. 2011, 61:30-43.
-
(2011)
Comput. Math. Appl.
, vol.61
, pp. 30-43
-
-
Ghoreishi, F.1
Yazdani, S.2
-
18
-
-
79960988872
-
Tau approximate solution of fractional partial differential equations
-
Vanani S.K., Aminataei A. Tau approximate solution of fractional partial differential equations. Comput. Math. Appl. 2011, 62:1075-1083.
-
(2011)
Comput. Math. Appl.
, vol.62
, pp. 1075-1083
-
-
Vanani, S.K.1
Aminataei, A.2
-
19
-
-
79953828683
-
On the convergence of spline collocation methods for solving fractional differential equations
-
Pedas A., Tamme E. On the convergence of spline collocation methods for solving fractional differential equations. J. Comput. Appl. Math. 2011, 235:3502-3514.
-
(2011)
J. Comput. Appl. Math.
, vol.235
, pp. 3502-3514
-
-
Pedas, A.1
Tamme, E.2
-
20
-
-
79953684270
-
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations
-
Esmaeili S., Shamsi M. A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 2011, 16:3646-3654.
-
(2011)
Commun. Nonlinear Sci. Numer. Simul.
, vol.16
, pp. 3646-3654
-
-
Esmaeili, S.1
Shamsi, M.2
-
21
-
-
79961002199
-
Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
-
Esmaeili S., Shamsi M., Luchko Y. Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials. Comput. Math. Appl. 2011, 62:918-929.
-
(2011)
Comput. Math. Appl.
, vol.62
, pp. 918-929
-
-
Esmaeili, S.1
Shamsi, M.2
Luchko, Y.3
-
23
-
-
79951948499
-
Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth- order differential equations
-
Doha E.H., Bhrawy A.H., Hafez R.M. Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth- order differential equations. Math. Comput. Model. 2011, 53:1820-1832.
-
(2011)
Math. Comput. Model.
, vol.53
, pp. 1820-1832
-
-
Doha, E.H.1
Bhrawy, A.H.2
Hafez, R.M.3
-
24
-
-
0742271179
-
On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials
-
Doha E.H. On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials. J. Phys. A Math. Gen. 2004, 37:657-675.
-
(2004)
J. Phys. A Math. Gen.
, vol.37
, pp. 657-675
-
-
Doha, E.H.1
-
26
-
-
3042709180
-
Multi-order fractional differential equations and their numerical solutions
-
Diethelm K., Ford N.J. Multi-order fractional differential equations and their numerical solutions. Appl. Math. Comput. 2004, 154:621-640.
-
(2004)
Appl. Math. Comput.
, vol.154
, pp. 621-640
-
-
Diethelm, K.1
Ford, N.J.2
-
27
-
-
77952705214
-
A collocation-shooting method for solving fractional boundary value problems
-
Mdallal Q.M., Syam M.I., Anwar M.N. A collocation-shooting method for solving fractional boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 2010, 15:3814-3822.
-
(2010)
Commun. Nonlinear Sci. Numer. Simul.
, vol.15
, pp. 3814-3822
-
-
Mdallal, Q.M.1
Syam, M.I.2
Anwar, M.N.3
-
28
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equation
-
Diethelm K., Ford N.J., Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equation. Nonlinear Dyn. 2002, 29:3-22.
-
(2002)
Nonlinear Dyn.
, vol.29
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
29
-
-
80052264305
-
Solving a multi-order fractional differential equation using homotopy analysis method
-
Jafari H., Das S., Tajadodi H. Solving a multi-order fractional differential equation using homotopy analysis method. J. King Saud University Sci. 2011, 23:151-155.
-
(2011)
J. King Saud University Sci.
, vol.23
, pp. 151-155
-
-
Jafari, H.1
Das, S.2
Tajadodi, H.3
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