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Volumn 385, Issue 1, 2012, Pages 111-124

On discrete sequential fractional boundary value problems

Author keywords

Boundary value problem; Cone; Discrete fractional calculus; Positive solution; Sequential fractional difference

Indexed keywords


EID: 80051790398     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2011.06.022     Document Type: Article
Times cited : (132)

References (46)
  • 1
    • 79953286192 scopus 로고    scopus 로고
    • Two-point boundary value problems for finite fractional difference equations
    • Atici F.M., Eloe P.W. Two-point boundary value problems for finite fractional difference equations. J. Difference Equ. Appl. 2011, 17:445-456.
    • (2011) J. Difference Equ. Appl. , vol.17 , pp. 445-456
    • Atici, F.M.1    Eloe, P.W.2
  • 2
    • 77049084247 scopus 로고    scopus 로고
    • Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative
    • Wei Z., Li Q., Che J. Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. J. Math. Anal. Appl. 2010, 367:260-272.
    • (2010) J. Math. Anal. Appl. , vol.367 , pp. 260-272
    • Wei, Z.1    Li, Q.2    Che, J.3
  • 3
    • 73249139676 scopus 로고    scopus 로고
    • On the concept of solution for fractional differential equations with uncertainty
    • Agarwal R.P., Lakshmikantham V., Nieto J.J. On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 2009, 72:2859-2862.
    • (2009) Nonlinear Anal. , vol.72 , pp. 2859-2862
    • Agarwal, R.P.1    Lakshmikantham, V.2    Nieto, J.J.3
  • 4
    • 70349490327 scopus 로고    scopus 로고
    • Calculus of variations with fractional derivatives and fractional integrals
    • Almeida R., Torres D.F.M. Calculus of variations with fractional derivatives and fractional integrals. Appl. Math. Lett. 2009, 22:1816-1820.
    • (2009) Appl. Math. Lett. , vol.22 , pp. 1816-1820
    • Almeida, R.1    Torres, D.F.M.2
  • 5
    • 71649104924 scopus 로고    scopus 로고
    • Fractional order differential equations on an unbounded domain
    • Arara A., et al. Fractional order differential equations on an unbounded domain. Nonlinear Anal. 2010, 72:580-586.
    • (2010) Nonlinear Anal. , vol.72 , pp. 580-586
    • Arara, A.1
  • 6
    • 0038405057 scopus 로고    scopus 로고
    • Existence of positive solutions of nonlinear fractional differential equations
    • Babakhani A., Daftardar-Gejji V. Existence of positive solutions of nonlinear fractional differential equations. J. Math. Anal. Appl. 2003, 278:434-442.
    • (2003) J. Math. Anal. Appl. , vol.278 , pp. 434-442
    • Babakhani, A.1    Daftardar-Gejji, V.2
  • 7
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Bai Z., Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 2005, 311:495-505.
    • (2005) J. Math. Anal. Appl. , vol.311 , pp. 495-505
    • Bai, Z.1    Lü, H.2
  • 8
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm K., Ford N. Analysis of fractional differential equations. J. Math. Anal. Appl. 2002, 265:229-248.
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.2
  • 9
    • 77953688007 scopus 로고    scopus 로고
    • Existence of a positive solution to a class of fractional differential equations
    • Goodrich C.S. Existence of a positive solution to a class of fractional differential equations. Appl. Math. Lett. 2010, 23:1050-1055.
    • (2010) Appl. Math. Lett. , vol.23 , pp. 1050-1055
    • Goodrich, C.S.1
  • 10
    • 77956899693 scopus 로고    scopus 로고
    • The profile of blowing-up solutions to a nonlinear system of fractional differential equations
    • Kirane M., Malik S.A. The profile of blowing-up solutions to a nonlinear system of fractional differential equations. Nonlinear Anal. 2010, 73:3723-3736.
    • (2010) Nonlinear Anal. , vol.73 , pp. 3723-3736
    • Kirane, M.1    Malik, S.A.2
  • 11
    • 77950866104 scopus 로고    scopus 로고
    • Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
    • Malinowska A., Torres D.F.M. Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative. Comput. Math. Appl. 2010, 59:3110-3116.
    • (2010) Comput. Math. Appl. , vol.59 , pp. 3110-3116
    • Malinowska, A.1    Torres, D.F.M.2
  • 12
    • 77955429536 scopus 로고    scopus 로고
    • Maximum principles for fractional differential equations derived from Mittag-Leffler functions
    • Nieto J.J. Maximum principles for fractional differential equations derived from Mittag-Leffler functions. Appl. Math. Lett. 2010, 23:1248-1251.
    • (2010) Appl. Math. Lett. , vol.23 , pp. 1248-1251
    • Nieto, J.J.1
  • 13
    • 67651094005 scopus 로고    scopus 로고
    • Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation
    • Xu X., Jiang D., Yuan C. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Nonlinear Anal. 2009, 71:4676-4688.
    • (2009) Nonlinear Anal. , vol.71 , pp. 4676-4688
    • Xu, X.1    Jiang, D.2    Yuan, C.3
  • 14
    • 74149083825 scopus 로고    scopus 로고
    • Initial value problems in discrete fractional calculus
    • Atici F.M., Eloe P.W. Initial value problems in discrete fractional calculus. Proc. Amer. Math. Soc. 2009, 137:981-989.
    • (2009) Proc. Amer. Math. Soc. , vol.137 , pp. 981-989
    • Atici, F.M.1    Eloe, P.W.2
  • 15
    • 78650178926 scopus 로고    scopus 로고
    • Solutions to a discrete right-focal fractional boundary value problem
    • Goodrich C.S. Solutions to a discrete right-focal fractional boundary value problem. Int. J. Difference Equ. 2010, 5:195-216.
    • (2010) Int. J. Difference Equ. , vol.5 , pp. 195-216
    • Goodrich, C.S.1
  • 16
    • 77953136599 scopus 로고    scopus 로고
    • Continuity of solutions to discrete fractional initial value problems
    • Goodrich C.S. Continuity of solutions to discrete fractional initial value problems. Comput. Math. Appl. 2010, 59:3489-3499.
    • (2010) Comput. Math. Appl. , vol.59 , pp. 3489-3499
    • Goodrich, C.S.1
  • 17
    • 77952557731 scopus 로고    scopus 로고
    • Modeling with fractional difference equations
    • Atici F.M., Şengül S. Modeling with fractional difference equations. J. Math. Anal. Appl. 2010, 369:1-9.
    • (2010) J. Math. Anal. Appl. , vol.369 , pp. 1-9
    • Atici, F.M.1    Şengül, S.2
  • 18
    • 78651241495 scopus 로고    scopus 로고
    • Necessary optimality conditions for fractional difference problems of the calculus of variations
    • Bastos N.R.O., et al. Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete Contin. Dyn. Syst. 2011, 29:417-437.
    • (2011) Discrete Contin. Dyn. Syst. , vol.29 , pp. 417-437
    • Bastos, N.R.O.1
  • 19
    • 79953294826 scopus 로고    scopus 로고
    • On a discrete fractional three-point boundary value problem
    • doi:10.1080/10236198.2010.503240
    • C.S. Goodrich, On a discrete fractional three-point boundary value problem, J. Difference Equ. Appl., doi:10.1080/10236198.2010.503240.
    • J. Difference Equ. Appl.
    • Goodrich, C.S.1
  • 20
    • 79951536621 scopus 로고    scopus 로고
    • Some new existence results for fractional difference equations
    • Goodrich C.S. Some new existence results for fractional difference equations. Int. J. Dyn. Syst. Differ. Equ. 2011, 3:145-162.
    • (2011) Int. J. Dyn. Syst. Differ. Equ. , vol.3 , pp. 145-162
    • Goodrich, C.S.1
  • 21
    • 78651230726 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
    • Goodrich C.S. Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. Comput. Math. Appl. 2011, 61:191-202.
    • (2011) Comput. Math. Appl. , vol.61 , pp. 191-202
    • Goodrich, C.S.1
  • 22
    • 78650170131 scopus 로고    scopus 로고
    • Existence of a positive solution to a system of discrete fractional boundary value problems
    • Goodrich C.S. Existence of a positive solution to a system of discrete fractional boundary value problems. Appl. Math. Comput. 2011, 217:4740-4753.
    • (2011) Appl. Math. Comput. , vol.217 , pp. 4740-4753
    • Goodrich, C.S.1
  • 23
    • 80051789735 scopus 로고    scopus 로고
    • A comparison result for the fractional difference operator, Int
    • in press.
    • C.S. Goodrich, A comparison result for the fractional difference operator, Int. J. Difference Equ. 6 (2011), in press.
    • (2011) J. Difference Equ. , vol.6
    • Goodrich, C.S.1
  • 24
    • 79953326334 scopus 로고    scopus 로고
    • On positive solutions to nonlocal fractional and integer-order difference equations
    • Goodrich C.S. On positive solutions to nonlocal fractional and integer-order difference equations. Appl. Anal. Discrete Math. 2011, 5:122-132.
    • (2011) Appl. Anal. Discrete Math. , vol.5 , pp. 122-132
    • Goodrich, C.S.1
  • 25
    • 78049333168 scopus 로고    scopus 로고
    • Discrete-time fractional variational problems
    • Bastos N.R.O., et al. Discrete-time fractional variational problems. Signal Process. 2011, 91:513-524.
    • (2011) Signal Process. , vol.91 , pp. 513-524
    • Bastos, N.R.O.1
  • 26
    • 79953318713 scopus 로고    scopus 로고
    • Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform
    • Bastos N.R.O., et al. Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform. Int. J. Math. Comput. 2011, 11:1-9.
    • (2011) Int. J. Math. Comput. , vol.11 , pp. 1-9
    • Bastos, N.R.O.1
  • 27
    • 78651236363 scopus 로고    scopus 로고
    • Positive solutions for a class of boundary value problems with fractional q-differences
    • Ferreira R.A.C. Positive solutions for a class of boundary value problems with fractional q-differences. Comput. Math. Appl. 2011, 61:367-373.
    • (2011) Comput. Math. Appl. , vol.61 , pp. 367-373
    • Ferreira, R.A.C.1
  • 28
    • 0036698158 scopus 로고    scopus 로고
    • Solutions to second-order three-point problems on time scales
    • Anderson D.R. Solutions to second-order three-point problems on time scales. J. Difference Equ. Appl. 2002, 8:673-688.
    • (2002) J. Difference Equ. Appl. , vol.8 , pp. 673-688
    • Anderson, D.R.1
  • 29
    • 22344455360 scopus 로고    scopus 로고
    • Positive solutions for a nonlinear functional dynamic equation on a time scale
    • Kaufmann E.R., Raffoul Y.N. Positive solutions for a nonlinear functional dynamic equation on a time scale. Nonlinear Anal. 2005, 62:1267-1276.
    • (2005) Nonlinear Anal. , vol.62 , pp. 1267-1276
    • Kaufmann, E.R.1    Raffoul, Y.N.2
  • 30
    • 33847653855 scopus 로고    scopus 로고
    • Multiple positive solutions for discrete nonlocal boundary value problems
    • Cheung W., Ren J., Wong P.J.Y., Zhao D. Multiple positive solutions for discrete nonlocal boundary value problems. J. Math. Anal. Appl. 2007, 330:900-915.
    • (2007) J. Math. Anal. Appl. , vol.330 , pp. 900-915
    • Cheung, W.1    Ren, J.2    Wong, P.J.Y.3    Zhao, D.4
  • 31
    • 0036538017 scopus 로고    scopus 로고
    • On Green's functions and positive solutions for boundary value problems on time scales
    • Atici F.M., Guseinov G. On Green's functions and positive solutions for boundary value problems on time scales. J. Comput. Appl. Math. 2002, 141:75-99.
    • (2002) J. Comput. Appl. Math. , vol.141 , pp. 75-99
    • Atici, F.M.1    Guseinov, G.2
  • 32
    • 0142031605 scopus 로고    scopus 로고
    • A stacked delta-nabla self-adjoint problem of even order
    • Anderson D.R., Hoffacker J. A stacked delta-nabla self-adjoint problem of even order. Math. Comput. Modelling 2003, 38(5-6):481-494.
    • (2003) Math. Comput. Modelling , vol.38 , Issue.5-6 , pp. 481-494
    • Anderson, D.R.1    Hoffacker, J.2
  • 33
    • 3242718005 scopus 로고    scopus 로고
    • Existence results for singular three point boundary value problems on time scales
    • DaCunha J.J., Davis J.M., Singh P.K. Existence results for singular three point boundary value problems on time scales. J. Math. Anal. Appl. 2004, 295:378-391.
    • (2004) J. Math. Anal. Appl. , vol.295 , pp. 378-391
    • DaCunha, J.J.1    Davis, J.M.2    Singh, P.K.3
  • 34
    • 1542406463 scopus 로고    scopus 로고
    • An even-order three-point boundary value problem on time scales
    • Anderson D.R., Avery R.I. An even-order three-point boundary value problem on time scales. J. Math. Anal. Appl. 2004, 291:514-525.
    • (2004) J. Math. Anal. Appl. , vol.291 , pp. 514-525
    • Anderson, D.R.1    Avery, R.I.2
  • 36
    • 34248209051 scopus 로고    scopus 로고
    • Self-adjoint boundary value problems on time scales and symmetric Green's functions
    • Guseinov G. Self-adjoint boundary value problems on time scales and symmetric Green's functions. Turkish J. Math. 2005, 29(4):365-380.
    • (2005) Turkish J. Math. , vol.29 , Issue.4 , pp. 365-380
    • Guseinov, G.1
  • 37
    • 33750624603 scopus 로고    scopus 로고
    • Existence of solutions for a cantilever beam problem
    • Anderson D.R., Hoffacker J. Existence of solutions for a cantilever beam problem. J. Math. Anal. Appl. 2006, 323:958-973.
    • (2006) J. Math. Anal. Appl. , vol.323 , pp. 958-973
    • Anderson, D.R.1    Hoffacker, J.2
  • 38
    • 36348980591 scopus 로고    scopus 로고
    • Existence of positive solutions for second-order m-point boundary value problems on time scales
    • Wang P., Wang Y. Existence of positive solutions for second-order m-point boundary value problems on time scales. Acta Math. Appl. Sin. Engl. Ser. 2006, 22:457-468.
    • (2006) Acta Math. Appl. Sin. Engl. Ser. , vol.22 , pp. 457-468
    • Wang, P.1    Wang, Y.2
  • 39
    • 37249009189 scopus 로고    scopus 로고
    • Reciprocity principle for even-order dynamic equations with mixed derivatives
    • Došlỳ O. Reciprocity principle for even-order dynamic equations with mixed derivatives. Dynam. Systems Appl. 2007, 16(4):697-708.
    • (2007) Dynam. Systems Appl. , vol.16 , Issue.4 , pp. 697-708
    • Došlỳ, O.1
  • 40
    • 79961012302 scopus 로고    scopus 로고
    • Sum and difference compositions and applications in discrete fractional calculus
    • Cubo in press.
    • M. Holm, Sum and difference compositions and applications in discrete fractional calculus, Cubo 3 (13) (2011), in press.
    • (2011) , vol.3 , Issue.13
    • Holm, M.1
  • 41
    • 77950548183 scopus 로고    scopus 로고
    • A transform method in discrete fractional calculus
    • Atici F.M., Eloe P.W. A transform method in discrete fractional calculus. Int. J. Difference Equ. 2007, 2:165-176.
    • (2007) Int. J. Difference Equ. , vol.2 , pp. 165-176
    • Atici, F.M.1    Eloe, P.W.2
  • 42
    • 85085399420 scopus 로고    scopus 로고
    • Discrete fractional calculus with the nabla operator
    • (Spec. Ed. I)
    • Atici F.M., Eloe P.W. Discrete fractional calculus with the nabla operator. Electron. J. Qual. Theory Differ. Equ. 2009, 3:1-12. (Spec. Ed. I).
    • (2009) Electron. J. Qual. Theory Differ. Equ. , vol.3 , pp. 1-12
    • Atici, F.M.1    Eloe, P.W.2
  • 45
    • 84966234102 scopus 로고
    • On the existence of positive solutions of ordinary differential equations
    • Erbe L.H., Wang H. On the existence of positive solutions of ordinary differential equations. Proc. Amer. Math. Soc. 1994, 120:743-748.
    • (1994) Proc. Amer. Math. Soc. , vol.120 , pp. 743-748
    • Erbe, L.H.1    Wang, H.2
  • 46
    • 33846042078 scopus 로고    scopus 로고
    • Positive solutions of nonlocal boundary value problems: a unified approach
    • Infante G., Webb J.R.L. Positive solutions of nonlocal boundary value problems: a unified approach. J. Lond. Math. Soc. 2006, 74:673-693.
    • (2006) J. Lond. Math. Soc. , vol.74 , pp. 673-693
    • Infante, G.1    Webb, J.R.L.2


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