-
1
-
-
70349490327
-
Calculus of variations with fractional derivatives and fractional integrals
-
R. Almeida, D. F. M. Torres: Calculus of variations with fractional derivatives and fractional integrals. Appl. Math. Lett., 22 (12) (2009), 1816-1820.
-
(2009)
Appl. Math. Lett.
, vol.22
, Issue.12
, pp. 1816-1820
-
-
Almeida, R.1
Torres, D.F.M.2
-
2
-
-
77957267794
-
Leitmann's direct method for fractional optimization problems
-
R. Almeida, D. F. M. Torres: Leitmann's direct method for fractional optimization problems. Appl. Math. Comput., 217 (3) (2010), 956-962.
-
(2010)
Appl. Math. Comput.
, vol.217
, Issue.3
, pp. 956-962
-
-
Almeida, R.1
Torres, D.F.M.2
-
3
-
-
77957362548
-
Necessary and sufficient conditions for the frac tional calculus of variations with Caputo derivatives
-
R. Almeida, D. F. M. Torres: Necessary and sufficient conditions for the frac tional calculus of variations with Caputo derivatives. Commun. Nonlinear Sci. Numer. Simul., 16 (3) (2011), 1490-1500.
-
(2011)
Commun. Nonlinear Sci. Numer. Simul.
, vol.16
, Issue.3
, pp. 1490-1500
-
-
Almeida, R.1
Torres, D.F.M.2
-
4
-
-
74149087492
-
Nabla discrete fractional calculus and nabla inequalities
-
G. A. Anastassiou: Nabla discrete fractional calculus and nabla inequalities. Math. Comput. Modelling, 51 (5-6) (2010), 562-571.
-
(2010)
Math. Comput. Modelling
, vol.51
, Issue.5-6
, pp. 562-571
-
-
Anastassiou, G.A.1
-
5
-
-
77950548183
-
A transform method in discrete fractional calculus
-
F. M. ATICI, P. W. ELOE: A transform method in discrete fractional calculus. Int. J. Difference Equ., 2 (2) (2007), 165-176.
-
(2007)
Int. J. Difference Equ.
, vol.2
, Issue.2
, pp. 165-176
-
-
Atici, F.M.1
Eloe, P.W.2
-
6
-
-
74149083825
-
Initial value problems in discrete fractional calculus
-
F. M. ATICI, P. W. Eloe: Initial value problems in discrete fractional calculus. Proc. Amer. Math. Soc., 137 (3) (2009), 981-989.
-
(2009)
Proc. Amer. Math. Soc.
, vol.137
, Issue.3
, pp. 981-989
-
-
Atici, F.M.1
Eloe, P.W.2
-
7
-
-
77952557731
-
Modeling with fractional difference equations
-
F. M. ATICI, S. SENGUL: Modeling with fractional difference equations. J. Math. Anal. Appl., 369 (1) (2010), 1-9.
-
(2010)
J. Math. Anal. Appl.
, vol.369
, Issue.1
, pp. 1-9
-
-
Atici, F.M.1
Sengul, S.2
-
8
-
-
78651241495
-
Necessary optimality conditions for fractional difference problems of the calculus of variations
-
N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete Contin. Dyn. Syst., 29 (2) (2011), 417-437.
-
(2011)
Discrete Contin. Dyn. Syst.
, vol.29
, Issue.2
, pp. 417-437
-
-
Bastos, N.R.O.1
Ferreira, R.A.C.2
Torres, D.F.M.3
-
9
-
-
78049333168
-
Discrete-time fractional variational problems
-
N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems. Signal Process., 91 (3) (2011), 513-524.
-
(2011)
Signal Process
, vol.91
, Issue.3
, pp. 513-524
-
-
Bastos, N.R.O.1
Ferreira, R.A.C.2
Torres, D.F.M.3
-
10
-
-
79953318713
-
Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform
-
N. R. O. Bastos, D. Mozyrska, D. F. M. Torres: Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform. Int. J. Math. Comput., 11 (J11) (2011), 1-9.
-
(2011)
Int. J. Math. Comput.
, vol.11
, Issue.J11
, pp. 1-9
-
-
Bastos, N.R.O.1
Mozyrska, D.2
Torres, D.F.M.3
-
11
-
-
79953323775
-
Combined delta-nabla sum operator in discrete fractional calculus
-
N. R. O. Bastos, D. F. M. Torres: Combined delta-nabla sum operator in discrete fractional calculus. Commun. Frac. Calc., 1 (1) (2010), 41-47.
-
(2010)
Commun. Frac. Calc.
, vol.1
, Issue.1
, pp. 41-47
-
-
Bastos, N.R.O.1
Torres, D.F.M.2
-
12
-
-
12844271148
-
Calculus of variations on time scales
-
M. Bohner: Calculus of variations on time scales. Dynam. Systems Appl., 13 (3-4) (2004), 339-349.
-
(2004)
Dynam. Systems Appl.
, vol.13
, Issue.3-4
, pp. 339-349
-
-
Bohner, M.1
-
13
-
-
34548583736
-
Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β)
-
R. A. EL-NABULSI, D. F. M. Torres: Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β). Math. Methods Appl. Sci., 30 (15) (2007), 1931-1939.
-
(2007)
Math. Methods Appl. Sci.
, vol.30
, Issue.15
, pp. 1931-1939
-
-
El-Nabulsi, R.A.1
Torres, D.F.M.2
-
14
-
-
44649143140
-
Fractional actionlike variational problems
-
R. A. EL-NABULSI, D. F. M. Torres: Fractional actionlike variational problems. J. Math. Phys., 49 (5) (2008), 053521, 7 pp.
-
(2008)
J. Math. Phys.
, vol.49
, Issue.5
-
-
El-Nabulsi, R.A.1
Torres, D.F.M.2
-
15
-
-
34250648556
-
A formulation of Noether's theorem for fractional problems of the calculus of variations
-
G. S. F. Frederico, D. F. M. Torres: A formulation of Noether's theorem for fractional problems of the calculus of variations. J. Math. Anal. Appl., 334 (2) (2007), 834-846.
-
(2007)
J. Math. Anal. Appl.
, vol.334
, Issue.2
, pp. 834-846
-
-
Frederico, G.S.F.1
Torres, D.F.M.2
-
16
-
-
46249125645
-
Fractional conservation laws in optimal control theory
-
G. S. F. Frederico, D. F. M. Torres: Fractional conservation laws in optimal control theory. Nonlinear Dynam., 53 (3) (2008), 215-222.
-
(2008)
Nonlinear Dynam
, vol.53
, Issue.3
, pp. 215-222
-
-
Frederico, G.S.F.1
Torres, D.F.M.2
-
17
-
-
77957259811
-
Fractional Noether's theorem in the Riesz-Caputo sense
-
G. S. F. Frederico, D. F. M. Torres: Fractional Noether's theorem in the Riesz-Caputo sense. Appl. Math. Comput., 217 (3) (2010), 1023-1033.
-
(2010)
Appl. Math. Comput.
, vol.217
, Issue.3
, pp. 1023-1033
-
-
Frederico, G.S.F.1
Torres, D.F.M.2
-
18
-
-
78650170131
-
Existence of a positive solution to a system of discrete fractional boundary value problems
-
C. S. Goodrich: Existence of a positive solution to a system of discrete fractional boundary value problems. Appl. Math. Comput., 217 (9) (2011), 4740-4753.
-
(2011)
Appl. Math. Comput.
, vol.217
, Issue.9
, pp. 4740-4753
-
-
Goodrich, C.S.1
-
19
-
-
84966257482
-
On a new definition of the fractional difference
-
H. L. GRAY, N. F. Zhang: On a new definition of the fractional difference. Math. Comp., 50 (182) (1988), 513-529.
-
(1988)
Math. Comp.
, vol.50
, Issue.182
, pp. 513-529
-
-
Gray, H.L.1
Zhang, N.F.2
-
20
-
-
33845595673
-
Discrete calculus of variations
-
Amer. Inst. Phys., Melville, NY
-
G. SH. Guseinov: Discrete calculus of variations. In "Global analysis and applied mathematics", 170-176, Amer. Inst. Phys., Melville, NY, 2004.
-
(2004)
Global analysis and applied mathematics
, pp. 170-176
-
-
Guseinov, S.H.G.1
-
22
-
-
77950866104
-
Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
-
A. B. Malinowska, D. F. M. Torres: Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative. Comput. Math. Appl. 59 (9) (2010), 3110-3116.
-
(2010)
Comput. Math. Appl.
, vol.59
, Issue.9
, pp. 3110-3116
-
-
Malinowska, A.B.1
Torres, D.F.M.2
-
23
-
-
0040209543
-
Representations of error terms in Jensen's and some related inequalities with applications
-
M. Merkle: Representations of error terms in Jensen's and some related inequalities with applications. J. Math. Anal. Appl., 231 (1) (1999), 76-90.
-
(1999)
J. Math. Anal. Appl.
, vol.231
, Issue.1
, pp. 76-90
-
-
Merkle, M.1
-
24
-
-
77949837723
-
Fractional difference calculus
-
Horwood, Chich-ester
-
K. S. Miller, B. ROSS: Fractional difference calculus. In "Univalent functions, frac tional calculus, and their applications (Koriyama, 1988)", 139-152, Horwood, Chich-ester, 1989.
-
(1989)
Univalent functions, frac tional calculus, and their applications (Koriyama, 1988)
, pp. 139-152
-
-
Miller, K.S.1
Ross, B.2
-
26
-
-
78049320912
-
Minimal modified energy control for fractional linear control systems with the Caputo derivative
-
D. Mozyrska, D. F. M. Torres: Minimal modified energy control for fractional linear control systems with the Caputo derivative. Carpathian J. Math., 26 (2) (2010), 210-221.
-
(2010)
Carpathian J. Math.
, vol.26
, Issue.2
, pp. 210-221
-
-
Mozyrska, D.1
Torres, D.F.M.2
-
27
-
-
78049334398
-
Modified optimal energy and initial memory of fractional continuous-time linear systems
-
D. Mozyrska, D. F. M. Torres: Modified optimal energy and initial memory of fractional continuous-time linear systems. Signal Process., 91 (3) (2011), 379-385.
-
(2011)
Signal Process
, vol.91
, Issue.3
, pp. 379-385
-
-
Mozyrska, D.1
Torres, D.F.M.2
-
28
-
-
52349114814
-
Fractional central differences and derivatives
-
M. D. Ortigueira: Fractional central differences and derivatives. J. Vib. Control, 14 (9-10) (2008), 1255-1266.
-
(2008)
J. Vib. Control.
, vol.14
, Issue.9-10
, pp. 1255-1266
-
-
Ortigueira, M.D.1
-
30
-
-
0003598080
-
-
Translated from the 1987 Russian original, Gordon and Breach, Yverdon
-
S. G. Samko, A. A. Kilbas, O. I. Marichev: Fractional integrals and derivatives. Translated from the 1987 Russian original, Gordon and Breach, Yverdon, 1993.
-
(1993)
Fractional integrals and derivatives
-
-
Samko, S.G.1
Kilbas, A.A.2
Marichev, O.I.3
|