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Volumn 5, Issue 1, 2011, Pages 110-121

Fractional h-difference equations arising from the calculus of variations

Author keywords

Euler Lagrange equations; Explicit solutions; Fractional difference calculus of variations; Fractional discrete calculus

Indexed keywords


EID: 79953329384     PISSN: 14528630     EISSN: None     Source Type: Journal    
DOI: 10.2298/AADM110131002F     Document Type: Article
Times cited : (175)

References (30)
  • 1
    • 70349490327 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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
  • 26
    • 78049320912 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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 scopus 로고    scopus 로고
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.