-
3
-
-
68249152474
-
Describing function based methods for predicting chaos in a class of fractional order differential equations
-
1176.34051 10.1007/s11071-008-9447-y
-
M.S. Tavazoei M. Haeri 2009 Describing function based methods for predicting chaos in a class of fractional order differential equations Nonlinear Dyn. 57 3 363 373 1176.34051 10.1007/s11071-008-9447-y
-
(2009)
Nonlinear Dyn.
, vol.57
, Issue.3
, pp. 363-373
-
-
Tavazoei, M.S.1
Haeri, M.2
-
4
-
-
0001154626
-
On dissipative systems and related variational principles
-
0003.01101 10.1103/PhysRev.38.815
-
H. Bateman 1931 On dissipative systems and related variational principles Phys. Rev. 38 4 815 819 0003.01101 10.1103/PhysRev.38.815
-
(1931)
Phys. Rev.
, vol.38
, Issue.4
, pp. 815-819
-
-
Bateman, H.1
-
5
-
-
0036701004
-
Formulation of Euler-Lagrange equations for fractional variational problems
-
1070.49013 10.1016/S0022-247X(02)00180-4
-
O.P. Agrawal 2002 Formulation of Euler-Lagrange equations for fractional variational problems J. Math. Anal. Appl. 272 1 368 379 1070.49013 10.1016/S0022-247X(02)00180-4
-
(2002)
J. Math. Anal. Appl.
, vol.272
, Issue.1
, pp. 368-379
-
-
Agrawal, O.P.1
-
6
-
-
15544379439
-
A general formulation and solution scheme for fractional optimal control problems
-
DOI 10.1007/s11071-004-3764-6
-
O.P. Agrawal 2004 A general formulation and solution scheme for fractional optimal control problems Nonlinear Dyn. 38 4 323 337 1121.70019 10.1007/s11071-004-3764-6 (Pubitemid 40400624)
-
(2004)
Nonlinear Dynamics
, vol.38
, Issue.1-4
, pp. 323-337
-
-
Agrawal, O.P.1
-
7
-
-
33746876366
-
Fractional variational calculus and the transversality conditions
-
DOI 10.1088/0305-4470/39/33/008, PII S0305447006218080, 008
-
O.P. Agrawal 2006 Fractional variational calculus and the transversality conditions J. Phys. A, Math. Gen. 39 10375 1097.49021 10.1088/0305-4470/39/33/ 008 (Pubitemid 44183559)
-
(2006)
Journal of Physics A: Mathematical and General
, vol.39
, Issue.33
, pp. 10375-10384
-
-
Agrawal, O.P.1
-
8
-
-
34250210234
-
Fractional variational calculus in terms of Riesz fractional derivatives
-
1125.26007 10.1088/1751-8113/40/24/003
-
O.P. Agrawal 2007 Fractional variational calculus in terms of Riesz fractional derivatives J. Phys. A, Math. Theor. 40 6287 1125.26007 10.1088/1751-8113/40/24/003
-
(2007)
J. Phys. A, Math. Theor.
, vol.40
, pp. 6287
-
-
Agrawal, O.P.1
-
9
-
-
4043139312
-
Lagrangians with linear velocities within Riemann-Liouville fractional derivatives
-
D. Baleanu T. Avkar 2004 Lagrangians with linear velocities within Riemann-Liouville fractional derivatives Nuovo Cim. B 119 73 79 (Pubitemid 39057448)
-
(2004)
Nuovo Cimento della Societa Italiana di Fisica B
, vol.119
, Issue.1
, pp. 73-79
-
-
Baleanu, D.1
Avkar, T.2
-
10
-
-
23344444772
-
Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
-
1122.70360 10.1238/Physica.Regular.072a00119
-
D. Baleanu S.I. Muslih 2005 Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives Phys Scr. 72 119 123 1122.70360 10.1238/Physica.Regular.072a00119
-
(2005)
Phys Scr.
, vol.72
, pp. 119-123
-
-
Baleanu, D.1
Muslih, S.I.2
-
11
-
-
33745514693
-
Hamiltonian formulation of classical fields within Riemann-Liouville fractional derivatives
-
DOI 10.1088/0031-8949/73/5/003, PII S0031894906195883, 003
-
S.I. Muslih D. Baleanu E. Rabei 2006 Hamiltonian formulation of classical fields within Riemann-Liouville fractional derivatives Phys. Scr. 73 436 438 1165.70310 10.1088/0031-8949/73/5/003 (Pubitemid 43958970)
-
(2006)
Physica Scripta
, vol.73
, Issue.5
, pp. 436-438
-
-
Muslih, S.I.1
Baleanu, D.2
Rabei, E.3
-
12
-
-
67449115682
-
Fractional WKB approximation
-
1176.70014 10.1007/s11071-008-9430-7
-
E.M. Rabei I.M.A. Altarazi S.I. Muslih D. Baleanu 2009 Fractional WKB approximation Nonlinear Dyn. 57 1-2 171 175 1176.70014 10.1007/s11071-008-9430-7
-
(2009)
Nonlinear Dyn.
, vol.57
, Issue.12
, pp. 171-175
-
-
Rabei, E.M.1
Altarazi, I.M.A.2
Muslih, S.I.3
Baleanu, D.4
-
13
-
-
77952842666
-
Fractional variational principles in action
-
10.1088/0031-8949/2009/T136/014006
-
D. Baleanu 2009 Fractional variational principles in action Phys. Scr. T136 014006 10.1088/0031-8949/2009/T136/014006
-
(2009)
Phys. Scr.
, vol.136
-
-
Baleanu, D.1
-
14
-
-
70349224466
-
Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations
-
1183.26006 10.1007/s11071-009-9486-z
-
M.A.E. Herzallah D. Baleanu 2009 Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations Nonlinear Dyn. 58 1-2 385 391 1183.26006 10.1007/s11071-009-9486-z
-
(2009)
Nonlinear Dyn.
, vol.58
, Issue.12
, pp. 385-391
-
-
Herzallah, M.A.E.1
Baleanu, D.2
-
15
-
-
70449529531
-
A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives
-
10.1016/j.cnsns.2009.05.023
-
D. Baleanu J.I. Trujillo 2010 A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives Commun. Nonlinear Sci. Numer. Simul. 15 5 1111 1115 10.1016/j.cnsns.2009.05.023
-
(2010)
Commun. Nonlinear Sci. Numer. Simul.
, vol.15
, Issue.5
, pp. 1111-1115
-
-
Baleanu, D.1
Trujillo, J.I.2
-
16
-
-
19944384253
-
Fractional Ginzburg-Landau equation for fractal media
-
DOI 10.1016/j.physa.2005.02.047, PII S0378437105002293
-
V.E. Tarasov G.M. Zaslavsky 2005 Fractional Ginzburg-Landau equation for fractal media Phys. A, Stat. Mech. Appl. 354 249 261 10.1016/j.physa.2005.02.047 (Pubitemid 40752473)
-
(2005)
Physica A: Statistical Mechanics and its Applications
, vol.354
, Issue.1-4
, pp. 249-261
-
-
Tarasov, V.E.1
Zaslavsky, G.M.2
-
17
-
-
33746269889
-
Nonholonomic constraints with fractional derivatives
-
DOI 10.1088/0305-4470/39/31/010, PII S0305447006206231, 010
-
V.E. Tarasov G.M. Zaslavsky 2006 Nonholonomic constraints with fractional derivatives J. Phys. A, Math. Gen. 39 31 9797 9815 1101.70011 10.1088/0305-4470/39/31/010 (Pubitemid 44102225)
-
(2006)
Journal of Physics A: Mathematical and General
, vol.39
, Issue.31
, pp. 9797-9815
-
-
Tarasov, V.E.1
Zaslavsky, G.M.2
-
18
-
-
15744376961
-
Fractional calculus description of non-linear viscoelastic behaviour of polymers
-
DOI 10.1007/s11071-004-3757-5
-
N. Heymans 2004 Fractional calculus description of non-linear viscoelastic behaviour of polymers Nonlinear Dyn. 38 1-2 221 231 1142.74312 10.1007/s11071-004-3757-5 (Pubitemid 40406781)
-
(2004)
Nonlinear Dynamics
, vol.38
, Issue.1-4
, pp. 221-231
-
-
Heymans, N.1
-
19
-
-
46249125645
-
Fractional conservation laws in optimal control theory
-
1170.49017 10.1007/s11071-007-9309-z
-
G.S.F. Frederico D.F.M. Torres 2008 Fractional conservation laws in optimal control theory Nonlinear Dyn. 53 3 215 222 1170.49017 10.1007/s11071-007-9309-z
-
(2008)
Nonlinear Dyn.
, vol.53
, Issue.3
, pp. 215-222
-
-
Frederico, G.S.F.1
Torres, D.F.M.2
-
20
-
-
59349109245
-
A fractional calculus interpretation of the fractional volatility model
-
1187.91231 10.1007/s11071-008-9372-0
-
R.V. Mendes 2009 A fractional calculus interpretation of the fractional volatility model Nonlinear Dyn. 55 4 395 399 1187.91231 10.1007/s11071-008-9372- 0
-
(2009)
Nonlinear Dyn.
, vol.55
, Issue.4
, pp. 395-399
-
-
Mendes, R.V.1
-
21
-
-
67449164063
-
Calculation of fractional derivatives of noisy data with genetic algorithms
-
1176.94016 10.1007/s11071-008-9436-1
-
J.A. Tenreiro Machado 2009 Calculation of fractional derivatives of noisy data with genetic algorithms Nonlinear Dyn. 57 1-2 253 260 1176.94016 10.1007/s11071-008-9436-1
-
(2009)
Nonlinear Dyn.
, vol.57
, Issue.12
, pp. 253-260
-
-
Tenreiro MacHado, J.A.1
-
22
-
-
77954348949
-
Analysis of a fractional order Van der Pol-like oscillator via describing function method
-
1204.70018 10.1007/s11071-009-9647-0
-
M. Attari M. Haeri M.S. Tavazoei 2010 Analysis of a fractional order Van der Pol-like oscillator via describing function method Nonlinear Dyn. 61 1-2 265 274 1204.70018 10.1007/s11071-009-9647-0
-
(2010)
Nonlinear Dyn.
, vol.61
, Issue.12
, pp. 265-274
-
-
Attari, M.1
Haeri, M.2
Tavazoei, M.S.3
-
23
-
-
53149136127
-
Special issue on "fractional Derivatives and their Applications"
-
Agrawal, O.P., Tenreiro Machado, J.A, Sabatier, J. (Guest Editors): Special issue on "Fractional Derivatives and their Applications". Nonlinear Dyn. 38(4) (2004)
-
(2004)
Nonlinear Dyn
, vol.38
, Issue.4
-
-
Agrawal, O.P.1
Tenreiro MacHado, J.A.2
Sabatier, J.3
-
24
-
-
84885710343
-
-
J. Sabatier O.P. Agrawal J.A. Tenreiro Machado (eds). Springer Dordrecht 1116.00014
-
Sabatier, J., Agrawal, O.P., Tenreiro Machado, J.A. (eds.): Advances in Fractional Calculus. Springer, Dordrecht (2007)
-
(2007)
Advances in Fractional Calculus
-
-
-
25
-
-
77952803107
-
Special issue on "fractional Differentiation and its Applications (FDA08)"
-
Baleanu, D., Tenreiro Machado, J.A. (Guest Editors): Special issue on "Fractional Differentiation and its Applications (FDA08)". Phys. Scr. T136 (2009)
-
(2009)
Phys. Scr. T136
-
-
Baleanu, D.1
Tenreiro MacHado, J.A.2
-
26
-
-
0001524186
-
On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves
-
D.J. Korteweg G. de Vries 1895 On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves Philos. Mag. 39 5 422
-
(1895)
Philos. Mag.
, vol.39
, Issue.5
, pp. 422
-
-
Korteweg, D.J.1
De Vries, G.2
-
27
-
-
67349172205
-
KdV Equation as an Euler-Poincare' equation
-
M.K. Fung 1997 KdV Equation as an Euler-Poincare' equation Chin. J. Phys. 35 6 789
-
(1997)
Chin. J. Phys.
, vol.35
, Issue.6
, pp. 789
-
-
Fung, M.K.1
-
31
-
-
0029288243
-
The exact solution of certain differential equations of fractional order by using operational calculus
-
0824.44011 10.1016/0898-1221(95)00031-S
-
Y. Luchko H.M. Srivastava 1995 The exact solution of certain differential equations of fractional order by using operational calculus Comput. Math. Appl. 29 73 85 0824.44011 10.1016/0898-1221(95)00031-S
-
(1995)
Comput. Math. Appl.
, vol.29
, pp. 73-85
-
-
Luchko, Y.1
Srivastava, H.M.2
-
32
-
-
0038405057
-
Existence of positive solutions of nonlinear fractional differential equations
-
DOI 10.1016/S0022-247X(02)00716-3
-
A. Babakhani V.D. Gejji 2003 Existence of positive solutions of nonlinear fractional differential equations J. Math. Anal. Appl. 278 434 442 1027.34003 10.1016/S0022-247X(02)00716-3 (Pubitemid 36530147)
-
(2003)
Journal of Mathematical Analysis and Applications
, vol.278
, Issue.2
, pp. 434-442
-
-
Babakhani, A.1
Daftardar-Gejji, V.2
-
33
-
-
0011651497
-
Fractional calculus and function spaces
-
D. Delbosco 1996 Fractional calculus and function spaces J. Fractal Calc. 6 45 53
-
(1996)
J. Fractal Calc.
, vol.6
, pp. 45-53
-
-
Delbosco, D.1
-
34
-
-
0037308989
-
Existence of positive solution for some class of nonlinear fractional differential equations
-
DOI 10.1016/S0022-247X(02)00583-8
-
S.Q. Zhang 2003 Existence of positive solution for some class of nonlinear fractional differential equations J. Math. Anal. Appl. 278 136 148 1026.34008 10.1016/S0022-247X(02)00583-8 (Pubitemid 36445950)
-
(2003)
Journal of Mathematical Analysis and Applications
, vol.278
, Issue.1
, pp. 136-148
-
-
Zhang, S.1
-
35
-
-
24944478244
-
An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method
-
DOI 10.1016/j.amc.2004.07.020, PII S0096300304005132
-
S. Saha Ray R.K. Bera 2005 An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method Appl. Math. Comput. 167 561 571 1082.65562 10.1016/j.amc.2004.07.020 (Pubitemid 41316348)
-
(2005)
Applied Mathematics and Computation
, vol.167
, Issue.1
, pp. 561-571
-
-
Ray, S.S.1
Bera, R.K.2
-
36
-
-
0032307661
-
Approximate analytical solution for seepage flow with fractional derivatives in porous media
-
0942.76077 10.1016/S0045-7825(98)00108-X
-
J.-H. He 1998 Approximate analytical solution for seepage flow with fractional derivatives in porous media Comput. Methods Appl. Mech. Eng. 167 57 68 0942.76077 10.1016/S0045-7825(98)00108-X
-
(1998)
Comput. Methods Appl. Mech. Eng.
, vol.167
, pp. 57-68
-
-
He, J.-H.1
-
37
-
-
38049162125
-
Variational iteration method for solving the space- and time-fractional KdV equation
-
S. Momani Z. Odibat A. Alawnah 2008 Variational iteration method for solving the space- and time-fractional KdV equation Numer. Methods Part. Differ. Equ. 24 1 261 271
-
(2008)
Numer. Methods Part. Differ. Equ.
, vol.24
, Issue.1
, pp. 261-271
-
-
Momani, S.1
Odibat, Z.2
Alawnah, A.3
-
38
-
-
60549112414
-
Variational iteration method for fractional heat- and wave-like equations
-
1172.35302 10.1016/j.nonrwa.2008.02.026
-
R.Y. Molliq M.S.M. Noorani I. Hashim 2009 Variational iteration method for fractional heat- and wave-like equations Nonlinear Anal., Real World Appl. 10 1854 1869 1172.35302 10.1016/j.nonrwa.2008.02.026
-
(2009)
Nonlinear Anal., Real World Appl.
, vol.10
, pp. 1854-1869
-
-
Molliq, R.Y.1
Noorani, M.S.M.2
Hashim, I.3
-
39
-
-
0006996396
-
General use of the Lagrange multiplier in non-linear mathematical physics
-
S. Nemat-Nasser (eds). Pergamon Press Oxford
-
Inokuti, M., Sekine, H., Mura, T.: General use of the Lagrange multiplier in non-linear mathematical physics. In: Nemat-Nasser, S. (ed.) Variational Method in the Mechanics of Solids. Pergamon Press, Oxford (1978)
-
(1978)
Variational Method in the Mechanics of Solids
-
-
Inokuti, M.1
Sekine, H.2
Mura, T.3
-
40
-
-
0007140364
-
A new approach to nonlinear partial differential equations
-
10.1016/S1007-5704(97)90007-1
-
J.-H. He 1997 A new approach to nonlinear partial differential equations Commun. Nonlinear Sci. Numer. Simul. 2 4 230 235 10.1016/S1007-5704(97)90007-1
-
(1997)
Commun. Nonlinear Sci. Numer. Simul.
, vol.2
, Issue.4
, pp. 230-235
-
-
He, J.-H.1
-
41
-
-
0000092673
-
Variational-iteration-a kind of nonlinear analytical technique: Some examples
-
05137891 10.1016/S0020-7462(98)00048-1
-
J.-H. He 1999 Variational-iteration-a kind of nonlinear analytical technique: some examples Int. J. Nonlinear Mech. 34 699 05137891 10.1016/S0020-7462(98)00048-1
-
(1999)
Int. J. Nonlinear Mech.
, vol.34
, pp. 699
-
-
He, J.-H.1
-
42
-
-
0031441505
-
Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics
-
J.-H. He 1997 Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbo-machinery aerodynamics Int. J. Turbo Jet-Engines 14 1 23 28 10.1515/TJJ.1997.14.1.23 (Pubitemid 127362293)
-
(1997)
International Journal of Turbo and Jet Engines
, vol.14
, Issue.1
, pp. 23-28
-
-
He, J.-H.1
-
43
-
-
0041621600
-
Variational principles for some nonlinear partial differential equations with variable coefficients
-
1135.35303 10.1016/S0960-0779(03)00265-0
-
J.-H. He 2004 Variational principles for some nonlinear partial differential equations with variable coefficients Chaos Solitons Fractals 19 847 851 1135.35303 10.1016/S0960-0779(03)00265-0
-
(2004)
Chaos Solitons Fractals
, vol.19
, pp. 847-851
-
-
He, J.-H.1
|