-
1
-
-
34548384362
-
Numerical methods for nonlinear partial differential equations of fractional order
-
DOI 10.1016/j.apm.2006.10.025, PII S0307904X06002800
-
Odibat Z., Momani S., Numerical methods for nonlinear partial differential equations of fractional order. Applied Mathematical Modelling 2008 32 1 28 39 2-s2.0-34548384362 10.1016/j.apm.2006.10.025 (Pubitemid 47355246)
-
(2008)
Applied Mathematical Modelling
, vol.32
, Issue.1
, pp. 28-39
-
-
Odibat, Z.1
Momani, S.2
-
2
-
-
33646878106
-
Analytical approach to linear fractional partial differential equations arising in fluid mechanics
-
DOI 10.1016/j.physleta.2006.02.048, PII S0375960106003148
-
Momani S., Odibat Z., Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Physics Letters A 2006 355 4-5 271 279 2-s2.0-33646878106 10.1016/j.physleta.2006.02.048 (Pubitemid 43783194)
-
(2006)
Physics Letters, Section A: General, Atomic and Solid State Physics
, vol.355
, Issue.4-5
, pp. 271-279
-
-
Momani, S.1
Odibat, Z.2
-
3
-
-
35348869861
-
Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
-
DOI 10.1016/j.chaos.2006.06.041, PII S0960077906005972
-
Odibat Z., Momani S., Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order. Chaos, Solitons & Fractals 2008 36 1 167 174 10.1016/j.chaos.2006.06.041 MR2372056 ZBL1152.34311 (Pubitemid 47576648)
-
(2008)
Chaos, Solitons and Fractals
, vol.36
, Issue.1
, pp. 167-174
-
-
Odibat, Z.1
Momani, S.2
-
4
-
-
55649102766
-
Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part
-
10.1016/j.camwa.2008.07.002 MR2474569 ZBL1165.65375
-
Hosseinnia S. H., Ranjbar A., Momani S., Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part. Computers & Mathematics with Applications 2008 56 12 3138 3149 10.1016/j.camwa.2008.07.002 MR2474569 ZBL1165.65375
-
(2008)
Computers & Mathematics with Applications
, vol.56
, Issue.12
, pp. 3138-3149
-
-
Hosseinnia, S.H.1
Ranjbar, A.2
Momani, S.3
-
5
-
-
37549050173
-
Solving systems of fractional differential equations by homotopy-perturbation method
-
10.1016/j.physleta.2007.07.059 MR2381825 ZBL1217.81080
-
Abdulaziz O., Hashim I., Momani S., Solving systems of fractional differential equations by homotopy-perturbation method. Physics Letters A 2008 372 4 451 459 10.1016/j.physleta.2007.07.059 MR2381825 ZBL1217.81080
-
(2008)
Physics Letters A
, vol.372
, Issue.4
, pp. 451-459
-
-
Abdulaziz, O.1
Hashim, I.2
Momani, S.3
-
6
-
-
0032307661
-
Approximate analytical solution for seepage flow with fractional derivatives in porous media
-
10.1016/S0045-7825(98)00108-X MR1665221 ZBL0942.76077
-
He J. H., Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 1998 167 1-2 57 68 10.1016/S0045-7825(98)00108-X MR1665221 ZBL0942.76077
-
(1998)
Computer Methods in Applied Mechanics and Engineering
, vol.167
, Issue.1-2
, pp. 57-68
-
-
He, J.H.1
-
7
-
-
0000092673
-
Variational iteration method - A kind of non-linear analytical technique: Some examples
-
2-s2.0-0000092673
-
He J. H., Variational iteration method-a kind of non-linear analytical technique: some examples. International Journal of Non-Linear Mechanics 1999 34 4 699 708 2-s2.0-0000092673
-
(1999)
International Journal of Non-Linear Mechanics
, vol.34
, Issue.4
, pp. 699-708
-
-
He, J.H.1
-
8
-
-
34250668369
-
Variational iteration method-Some recent results and new interpretations
-
DOI 10.1016/j.cam.2006.07.009, PII S0377042706004559, Variational Iteration Method-Reality, Potential, and Challenges
-
He J. H., Variational iteration method-some recent results and new interpretations. Journal of Computational and Applied Mathematics 2007 207 1 3 17 10.1016/j.cam.2006.07.009 MR2332941 ZBL1119.65049 (Pubitemid 46935380)
-
(2007)
Journal of Computational and Applied Mathematics
, vol.207
, Issue.1
, pp. 3-17
-
-
He, J.-H.1
-
9
-
-
80052270048
-
A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
-
10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
-
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. Computers & Mathematics with Applications 2011 62 5 2364 2373 10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
-
(2011)
Computers & Mathematics with Applications
, vol.62
, Issue.5
, pp. 2364-2373
-
-
Doha, E.H.1
Bhrawy, A.H.2
Ezz-Eldien, S.S.3
-
10
-
-
84864987975
-
A shifted Legendre spectral method for fractional-order multi-point boundary value problems
-
article 8 10.1186/1687-1847-2012-8 MR2892994
-
Bhrawy A. H., Al-Shomrani M. M., A shifted Legendre spectral method for fractional-order multi-point boundary value problems. Advances in Difference Equations 2012 2012 article 8 19 10.1186/1687-1847-2012-8 MR2892994
-
(2012)
Advances in Difference Equations
, vol.2012
, pp. 19
-
-
Bhrawy, A.H.1
Al-Shomrani, M.M.2
-
11
-
-
84872169204
-
An adaptive pseudospectral method for fractional order boundary value problems
-
10.1155/2012/381708 381708 MR3004873 ZBL1261.34009
-
Maleki M., Hashim I., Tavassoli Kajani M., Abbasbandy S., An adaptive pseudospectral method for fractional order boundary value problems. Abstract and Applied Analysis 2012 2012 19 10.1155/2012/381708 381708 MR3004873 ZBL1261.34009
-
(2012)
Abstract and Applied Analysis
, vol.2012
, pp. 19
-
-
Maleki, M.1
Hashim, I.2
Tavassoli Kajani, M.3
Abbasbandy, S.4
-
12
-
-
84880177806
-
Two efficient generalized Laguerre spectral algorithms for fractional initial value problems
-
10.1155/2013/546502 546502 MR3066294
-
Baleanu D., Bhrawy A. H., Taha T. M., Two efficient generalized Laguerre spectral algorithms for fractional initial value problems. Abstract and Applied Analysis 2013 2013 10 10.1155/2013/546502 546502 MR3066294
-
(2013)
Abstract and Applied Analysis
, vol.2013
, pp. 10
-
-
Baleanu, D.1
Bhrawy, A.H.2
Taha, T.M.3
-
13
-
-
84884273927
-
A new legendre spectral galerkin and pseudo-spectral approximations for fractional initial value problems
-
306746 10.1155/2013/306746
-
Bhrawy A. H., Alghamdi M. A., A new legendre spectral galerkin and pseudo-spectral approximations for fractional initial value problems. Abstract and Applied Analysis 2013 2013 10 306746 10.1155/2013/306746
-
(2013)
Abstract and Applied Analysis
, vol.2013
, pp. 10
-
-
Bhrawy, A.H.1
Alghamdi, M.A.2
-
14
-
-
74249095517
-
A new operational matrix for solving fractional-order differential equations
-
10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
-
Saadatmandi A., Dehghan M., A new operational matrix for solving fractional-order differential equations. Computers & Mathematics with Applications 2010 59 3 1326 1336 10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
-
(2010)
Computers & Mathematics with Applications
, vol.59
, Issue.3
, pp. 1326-1336
-
-
Saadatmandi, A.1
Dehghan, M.2
-
15
-
-
79961168894
-
A quadrature tau method for fractional differential equations with variable coefficients
-
10.1016/j.aml.2011.06.016 MR2826154 ZBL1269.65068
-
Bhrawy A. H., Alofi A. S., Ezz-Eldien S. S., A quadrature tau method for fractional differential equations with variable coefficients. Applied Mathematics Letters 2011 24 12 2146 2152 10.1016/j.aml.2011.06.016 MR2826154 ZBL1269.65068
-
(2011)
Applied Mathematics Letters
, vol.24
, Issue.12
, pp. 2146-2152
-
-
Bhrawy, A.H.1
Alofi, A.S.2
Ezz-Eldien, S.S.3
-
16
-
-
84866046515
-
The operational matrix of fractional integration for shifted Chebyshev polynomials
-
10.1016/j.aml.2012.01.027 MR2971394 ZBL1255.65147
-
Bhrawy A. H., Alofi A. S., The operational matrix of fractional integration for shifted Chebyshev polynomials. Applied Mathematics Letters 2013 26 1 25 31 10.1016/j.aml.2012.01.027 MR2971394 ZBL1255.65147
-
(2013)
Applied Mathematics Letters
, vol.26
, Issue.1
, pp. 25-31
-
-
Bhrawy, A.H.1
Alofi, A.S.2
-
17
-
-
84873098191
-
Numerical solution of the Bagley-Torvik equation by the Bessel collocation method
-
10.1002/mma.2588
-
Yüzbasi S., Numerical solution of the Bagley-Torvik equation by the Bessel collocation method. Mathematical Methods in the Applied Sciences 2013 36 3 300 312 10.1002/mma.2588
-
(2013)
Mathematical Methods in the Applied Sciences
, vol.36
, Issue.3
, pp. 300-312
-
-
Yüzbasi, S.1
-
18
-
-
67349274987
-
A wavelet operational method for solving fractional partial differential equations numerically
-
10.1016/j.amc.2009.03.066 MR2537437 ZBL1169.65127
-
Wu J. L., A wavelet operational method for solving fractional partial differential equations numerically. Applied Mathematics and Computation 2009 214 1 31 40 10.1016/j.amc.2009.03.066 MR2537437 ZBL1169.65127
-
(2009)
Applied Mathematics and Computation
, vol.214
, Issue.1
, pp. 31-40
-
-
Wu, J.L.1
-
19
-
-
74249095517
-
A new operational matrix for solving fractional-order differential equations
-
10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
-
Saadatmandi A., Dehghan M., A new operational matrix for solving fractional-order differential equations. Computers & Mathematics with Applications 2010 59 3 1326 1336 10.1016/j.camwa.2009.07.006 MR2579495 ZBL1189.65151
-
(2010)
Computers & Mathematics with Applications
, vol.59
, Issue.3
, pp. 1326-1336
-
-
Saadatmandi, A.1
Dehghan, M.2
-
20
-
-
79960994078
-
Application of Legendre wavelets for solving fractional differential equations
-
10.1016/j.camwa.2011.04.024 MR2824691 ZBL1228.65253
-
Jafari H., Yousefi S. A., Firoozjaee M. A., Momani S., Khalique C. M., Application of Legendre wavelets for solving fractional differential equations. Computers & Mathematics with Applications 2011 62 3 1038 1045 10.1016/j.camwa.2011.04.024 MR2824691 ZBL1228.65253
-
(2011)
Computers & Mathematics with Applications
, vol.62
, Issue.3
, pp. 1038-1045
-
-
Jafari, H.1
Yousefi, S.A.2
Firoozjaee, M.A.3
Momani, S.4
Khalique, C.M.5
-
21
-
-
77949492283
-
Solving a nonlinear fractional differential equation using Chebyshev wavelets
-
10.1016/j.cnsns.2009.09.020 MR2602712 ZBL1222.65087
-
Li Y., Solving a nonlinear fractional differential equation using Chebyshev wavelets. Communications in Nonlinear Science and Numerical Simulation 2010 15 9 2284 2292 10.1016/j.cnsns.2009.09.020 MR2602712 ZBL1222.65087
-
(2010)
Communications in Nonlinear Science and Numerical Simulation
, vol.15
, Issue.9
, pp. 2284-2292
-
-
Li, Y.1
-
22
-
-
84880168892
-
An operational matrix based on Legendre polynomials for solving fuzzy fractional-order differential equations
-
10.1155/2013/505903 505903 MR3068179
-
Ahmadian A., Suleiman M., Salahshour S., An operational matrix based on Legendre polynomials for solving fuzzy fractional-order differential equations. Abstract and Applied Analysis 2013 2013 29 10.1155/2013/505903 505903 MR3068179
-
(2013)
Abstract and Applied Analysis
, vol.2013
, pp. 29
-
-
Ahmadian, A.1
Suleiman, M.2
Salahshour, S.3
-
24
-
-
84893174112
-
An operational matrix of fractional integration of the Laguerre polynomials and its application on a semi-infinite interval
-
article 41 10.1186/2251-7456-6-41 MR3030359 ZBL06194915
-
Bhrawy A. H., Taha T. M., An operational matrix of fractional integration of the Laguerre polynomials and its application on a semi-infinite interval. Mathematical Sciences 2012 6 article 41 7 10.1186/2251-7456-6-41 MR3030359 ZBL06194915
-
(2012)
Mathematical Sciences
, vol.6
, pp. 7
-
-
Bhrawy, A.H.1
Taha, T.M.2
-
25
-
-
84873337961
-
A new modified generalized Laguerre operational matrix of fractional integration for solving fractional differential equations on the half line
-
10.1186/1687-1847-2012-179 MR3016069 12
-
Bhrawy A. H., Alghamdi M. M., Taha T. M., A new modified generalized Laguerre operational matrix of fractional integration for solving fractional differential equations on the half line. Advances in Difference Equations 2012 2012:179, 12 10.1186/1687-1847-2012-179 MR3016069
-
(2012)
Advances in Difference Equations
, pp. 2012179
-
-
Bhrawy, A.H.1
Alghamdi, M.M.2
Taha, T.M.3
-
26
-
-
84870242888
-
An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations
-
10.1016/j.apm.2012.03.033 MR3002211
-
Kazem S., An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations. Applied Mathematical Modelling 2013 37 3 1126 1136 10.1016/j.apm.2012.03.033 MR3002211
-
(2013)
Applied Mathematical Modelling
, vol.37
, Issue.3
, pp. 1126-1136
-
-
Kazem, S.1
-
27
-
-
84872596071
-
On the fractional order Rodrigues formula for the Legendre polynomials
-
MR2906167 ZBL1239.26008
-
Rida S. Z., Yousef A. M., On the fractional order Rodrigues formula for the Legendre polynomials. Advances and Applications in Mathematical Sciences 2011 10 5 509 517 MR2906167 ZBL1239.26008
-
(2011)
Advances and Applications in Mathematical Sciences
, vol.10
, Issue.5
, pp. 509-517
-
-
Rida, S.Z.1
Yousef, A.M.2
-
28
-
-
84872602206
-
Fractional-order Legendre functions for solving fractional-order differential equations
-
10.1016/j.apm.2012.10.026 MR3020667
-
Kazem S., Abbasbandy S., Kumar S., Fractional-order Legendre functions for solving fractional-order differential equations. Applied Mathematical Modelling 2013 37 7 5498 5510 10.1016/j.apm.2012.10.026 MR3020667
-
(2013)
Applied Mathematical Modelling
, vol.37
, Issue.7
, pp. 5498-5510
-
-
Kazem, S.1
Abbasbandy, S.2
Kumar, S.3
-
30
-
-
0242354999
-
Geometric and physical interpretation of fractional integration and fractional differentiation
-
MR1967839 ZBL1042.26003
-
Podlubny I., Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calculus & Applied Analysis 2002 5 4 367 386 MR1967839 ZBL1042.26003
-
(2002)
Fractional Calculus & Applied Analysis
, vol.5
, Issue.4
, pp. 367-386
-
-
Podlubny, I.1
-
31
-
-
73449118638
-
Legendre wavelet method for numerical solutions of partial differential equations
-
10.1002/num.20417 MR2588907 ZBL1186.65152
-
Liu N., Lin E. B., Legendre wavelet method for numerical solutions of partial differential equations. Numerical Methods for Partial Differential Equations 2010 26 1 81 94 10.1002/num.20417 MR2588907 ZBL1186.65152
-
(2010)
Numerical Methods for Partial Differential Equations
, vol.26
, Issue.1
, pp. 81-94
-
-
Liu, N.1
Lin, E.B.2
-
32
-
-
84875755518
-
Couple of the variational iteration method and Legendre wavelets for nonlinear partial differential equations
-
10.1155/2013/157956 157956 MR3032260 ZBL1266.65218
-
Yin F., Song J., Cao X., Lu F., Couple of the variational iteration method and Legendre wavelets for nonlinear partial differential equations. Journal of Applied Mathematics 2013 2013 11 10.1155/2013/157956 157956 MR3032260 ZBL1266.65218
-
(2013)
Journal of Applied Mathematics
, vol.2013
, pp. 11
-
-
Yin, F.1
Song, J.2
Cao, X.3
Lu, F.4
-
33
-
-
84875236585
-
Challenge in the variational iteration method - A new approach to identification of the Lagrange multipliers
-
10.1016/j.jksus.2012.12.002
-
Wu G. C., Challenge in the variational iteration method-a new approach to identification of the Lagrange multipliers. Journal of King Saud University 2013 25 175 178 10.1016/j.jksus.2012.12.002
-
(2013)
Journal of King Saud University
, vol.25
, pp. 175-178
-
-
Wu, G.C.1
-
34
-
-
84897110293
-
A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations
-
10.1002/mma.2834
-
Yin F., Song J., Lu F., A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations. Mathematical Methods in the Applied Sciences 2013 10.1002/mma.2834
-
(2013)
Mathematical Methods in the Applied Sciences
-
-
Yin, F.1
Song, J.2
Lu, F.3
-
35
-
-
84890059821
-
Decomposition method for fractional partial differential equation (PDEs) using Laplace transformation
-
10.5897/IJPS12.727
-
Imran N., Mohyud-Din S. T., Decomposition method for fractional partial differential equation (PDEs) using Laplace transformation. International Journal of Physical Sciences 2013 8 16 684 688 10.5897/IJPS12.727
-
(2013)
International Journal of Physical Sciences
, vol.8
, Issue.16
, pp. 684-688
-
-
Imran, N.1
Mohyud-Din, S.T.2
-
36
-
-
84873402475
-
Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation
-
010201 10.1088/1674-1056/22/1/010201
-
Gepreel K. A., Mohamed M. S., Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation. Chinese Physics B 2013 22 1 010201 10.1088/1674-1056/22/1/010201
-
(2013)
Chinese Physics B
, vol.22
, Issue.1
-
-
Gepreel, K.A.1
Mohamed, M.S.2
-
37
-
-
84858129820
-
A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders
-
2-s2.0-84858129820 10.1155/2012/581481 581481
-
El-Sayed A. M. A., Elsaid A., Hammad D., A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders. Journal of Applied Mathematics 2012 2012 13 2-s2.0-84858129820 10.1155/2012/581481 581481
-
(2012)
Journal of Applied Mathematics
, vol.2012
, pp. 13
-
-
El-Sayed, A.M.A.1
Elsaid, A.2
Hammad, D.3
-
38
-
-
47849126401
-
A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
-
10.1016/j.cam.2007.07.033 MR2444156 ZBL1148.65099
-
Momani S., Odibat Z., A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor's formula. Journal of Computational and Applied Mathematics 2008 220 1-2 85 95 10.1016/j.cam.2007.07.033 MR2444156 ZBL1148.65099
-
(2008)
Journal of Computational and Applied Mathematics
, vol.220
, Issue.1-2
, pp. 85-95
-
-
Momani, S.1
Odibat, Z.2
-
39
-
-
84874902089
-
Fractional variational iteration method versus Adomian's decomposition method in some fractional partial differential equations
-
10.1155/2013/392567 392567 MR3032203 ZBL1266.35141
-
Song J., Yin F., Cao X., Lu F., Fractional variational iteration method versus Adomian's decomposition method in some fractional partial differential equations. Journal of Applied Mathematics 2013 2013 10 10.1155/2013/392567 392567 MR3032203 ZBL1266.35141
-
(2013)
Journal of Applied Mathematics
, vol.2013
, pp. 10
-
-
Song, J.1
Yin, F.2
Cao, X.3
Lu, F.4
|