메뉴 건너뛰기




Volumn 62, Issue 3, 2011, Pages 1228-1237

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

Author keywords

resolvent family; Controllability; Fractional differential equations; Phase space axioms

Indexed keywords

FIXED POINT THEOREMS; FRACTIONAL DIFFERENTIAL EQUATIONS; FUNCTIONAL DIFFERENTIAL EQUATIONS; GLOBAL SOLUTIONS; INFINITE DELAY; NONLINEAR ALTERNATIVE OF LERAY-SCHAUDER TYPE; PHASE SPACES; RESOLVENT FAMILY;

EID: 79960999852     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.03.039     Document Type: Article
Times cited : (36)

References (45)
  • 1
    • 53949107192 scopus 로고    scopus 로고
    • Almost automorphic mild solutions to fractional differential equations
    • D. Araya, and C. Lizama Almost automorphic mild solutions to fractional differential equations Nonlinear Anal. 69 2008 3692 3705
    • (2008) Nonlinear Anal. , vol.69 , pp. 3692-3705
    • Araya, D.1    Lizama, C.2
  • 2
    • 34247323827 scopus 로고    scopus 로고
    • Fractional differential equations as alternative models to nonlinear differential equations
    • DOI 10.1016/j.amc.2006.08.105, PII S0096300306011398
    • B. Bonila, M. Rivero, L. Rodriquez-Germa, and J.J. Trujilio Fractional differential equations as alternative models to nonlinear differential equations Appl. Math. Comput. 187 2007 79 88 (Pubitemid 46635706)
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.1 SPEC. ISSUE , pp. 79-88
    • Bonilla, B.1    Rivero, M.2    Rodriguez-Germa, L.3    Trujillo, J.J.4
  • 3
    • 70449526839 scopus 로고    scopus 로고
    • An approach via fractional analysis to non-linearity induced by coarse-graining in space
    • G. Jumarie An approach via fractional analysis to non-linearity induced by coarse-graining in space Nonlinear Anal. RWA 11 2010 535 546
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 535-546
    • Jumarie, G.1
  • 4
    • 59849083895 scopus 로고    scopus 로고
    • Integral equations and initial value problems for nonlinear differential equations of fractional order
    • N. Kosmatov Integral equations and initial value problems for nonlinear differential equations of fractional order Nonlinear Anal. 70 2009 2521 2529
    • (2009) Nonlinear Anal. , vol.70 , pp. 2521-2529
    • Kosmatov, N.1
  • 6
    • 67650110018 scopus 로고    scopus 로고
    • A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
    • (Article ID 981728, 47 pages)
    • R.P. Agarwal, M. Belmekki, and M. Benchohra A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative Adv. Difference Equ. 2009 2009 (Article ID 981728, 47 pages)
    • (2009) Adv. Difference Equ. , vol.2009
    • Agarwal, R.P.1    Belmekki, M.2    Benchohra, M.3
  • 7
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and their approximations
    • J.H. He Some applications of nonlinear fractional differential equations and their approximations Bull. Sci. Technol. 15 2 1999 86 90
    • (1999) Bull. Sci. Technol. , vol.15 , Issue.2 , pp. 86-90
    • He, J.H.1
  • 8
    • 0001983732 scopus 로고    scopus 로고
    • Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics
    • A. Carpinteri, F. Mainardi, Springer-Verlag New York
    • F. Mainardi Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer-Verlag New York 291 348
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 13
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • 10.1007/s10440-008-9356-6
    • R.P. Agarwal, M. Benchohra, and S. Hamani A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta Appl. Math. 2010 10.1007/s10440-008-9356-6
    • (2010) Acta Appl. Math.
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 14
    • 74149092568 scopus 로고    scopus 로고
    • Existence of fractional neutral functional differential equations
    • R.P. Agarwal, Y. Zhou, and Y. He Existence of fractional neutral functional differential equations Comput. Math. Appl. 59 2010 1095 1100
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1095-1100
    • Agarwal, R.P.1    Zhou, Y.2    He, Y.3
  • 15
    • 70349131961 scopus 로고    scopus 로고
    • Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions
    • B. Ahmad, and J.J. Nieto Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions Comput. Math. Appl 58 2009 1838 1843
    • (2009) Comput. Math. Appl , vol.58 , pp. 1838-1843
    • Ahmad, B.1    Nieto, J.J.2
  • 16
    • 64249112537 scopus 로고    scopus 로고
    • Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions
    • 11 pages. Article ID 708576
    • B. Ahmad, and J.J. Nieto Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions Bound. Value Probl. 2009 2009 11 pages. Article ID 708576
    • (2009) Bound. Value Probl. , vol.2009
    • Ahmad, B.1    Nieto, J.J.2
  • 17
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • DOI 10.1016/j.jmaa.2005.02.052, PII S0022247X05001733
    • Z. Bai, and H. L Positive solutions for boundary value problem of nonlinear fractional differential equations J. Math. Anal. Appl. 311 2005 495 505 (Pubitemid 41350217)
    • (2005) Journal of Mathematical Analysis and Applications , vol.311 , Issue.2 , pp. 495-505
    • Bai, Z.1    Lu, H.2
  • 18
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 2008 1340 1350
    • (2008) J. Math. Anal. Appl. , vol.338 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 19
    • 58049138945 scopus 로고    scopus 로고
    • Some new existence results for fractional differential inclusions with boundary conditions
    • Y.K. Chang, and J.J. Nieto Some new existence results for fractional differential inclusions with boundary conditions Math. Comput. Modelling 49 2009 605 609
    • (2009) Math. Comput. Modelling , vol.49 , pp. 605-609
    • Chang, Y.K.1    Nieto, J.J.2
  • 20
    • 51349139941 scopus 로고    scopus 로고
    • Theory of fractional functional differential equation
    • V. Lakshmikantham Theory of fractional functional differential equation Nonlinear Anal. 69 2008 3337 3343
    • (2008) Nonlinear Anal. , vol.69 , pp. 3337-3343
    • Lakshmikantham, V.1
  • 21
    • 51349163878 scopus 로고    scopus 로고
    • Theory of fractional differential equations in a Banach space
    • V. Lakshmikantham, and J.V. Devi Theory of fractional differential equations in a Banach space Eur. J. Pure Appl. Math. 1 1 2008 38 45
    • (2008) Eur. J. Pure Appl. Math. , vol.1 , Issue.1 , pp. 38-45
    • Lakshmikantham, V.1    Devi, J.V.2
  • 22
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • V. Lakshmikantham, and A.S. Vatsala Basic theory of fractional differential equations Nonlinear Anal. 69 2008 2677 2682
    • (2008) Nonlinear Anal. , vol.69 , pp. 2677-2682
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 23
    • 45049084850 scopus 로고    scopus 로고
    • General uniqueness and monotone iteration technique in fractional differential equations
    • V. Lakshmikantham, and A.S. Vatsala General uniqueness and monotone iteration technique in fractional differential equations Appl. Math. Lett. 21 2008 828 834
    • (2008) Appl. Math. Lett. , vol.21 , pp. 828-834
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 24
    • 59249101044 scopus 로고    scopus 로고
    • Mild solutions for semilinear fractional differential equations
    • G.M. Mophou, and G.M. N'Guérékata Mild solutions for semilinear fractional differential equations Electron. J. Differential Equations 2009 21 2009 1 9
    • (2009) Electron. J. Differential Equations , vol.2009 , Issue.21 , pp. 1-9
    • Mophou, G.M.1    N'Guérékata, G.M.2
  • 25
    • 77049086990 scopus 로고    scopus 로고
    • Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay
    • G.M. Mophou, and G.M. N'Guérékata Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay Appl. Math. Comput. 216 2010 61 69
    • (2010) Appl. Math. Comput. , vol.216 , pp. 61-69
    • Mophou, G.M.1    N'Guérékata, G.M.2
  • 26
    • 58149231350 scopus 로고    scopus 로고
    • A Cauchy problem for some fractional abstract differential equations with non local conditions
    • G.M. N'Guérékata A Cauchy problem for some fractional abstract differential equations with non local conditions Nonlinear Anal. 70 5 2009 1873 1876
    • (2009) Nonlinear Anal. , vol.70 , Issue.5 , pp. 1873-1876
    • N'Guérékata, G.M.1
  • 27
    • 77049086990 scopus 로고    scopus 로고
    • Remarks on the paper: Existence of mild solutions of some neutral fractional functional evolution equations with infinite delay
    • Int. J. Evol. Equ., 5(3) (2010), 13
    • G.M. N'Guérékata Remarks on the paper: Existence of mild solutions of some neutral fractional functional evolution equations with infinite delay Appl. Math. Comput. 216 2010 61 69 Int. J. Evol. Equ., 5(3) (2010), 13
    • (2010) Appl. Math. Comput. , vol.216 , pp. 61-69
    • N'Guérékata, G.M.1
  • 28
    • 67349088414 scopus 로고    scopus 로고
    • Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives
    • S. Zhang Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives Nonlinear Anal. 71 2009 2087 2093
    • (2009) Nonlinear Anal. , vol.71 , pp. 2087-2093
    • Zhang, S.1
  • 29
    • 67349177003 scopus 로고    scopus 로고
    • Existence and uniqueness for fractional neutral differential equations with infinite delay
    • Y. Zhong, J. Feng, and J. Li Existence and uniqueness for fractional neutral differential equations with infinite delay Nonlinear Anal. 71 2009 3249 3256
    • (2009) Nonlinear Anal. , vol.71 , pp. 3249-3256
    • Zhong, Y.1    Feng, J.2    Li, J.3
  • 31
    • 33748896254 scopus 로고    scopus 로고
    • Remarks on the paper "Controllability of second order differential inclusion in Banach spaces" [J. Math. Anal. Appl. 285 (2003) 537-550]
    • DOI 10.1016/j.jmaa.2005.11.070, PII S0022247X05012825
    • K. Balachandran, and J.H. Kim Remarks on the paper "Controllability of second order differential inclusion in Banach spaces" [J. Math. Anal. Appl. 285, 537550 (2003)] J. Math. Anal. Appl. 324 2006 746 749 (Pubitemid 44426305)
    • (2006) Journal of Mathematical Analysis and Applications , vol.324 , Issue.1 , pp. 746-749
    • Balachandran, K.1    Kim, J.-H.2
  • 32
    • 14044253446 scopus 로고    scopus 로고
    • Controllability results for functional semilinear differential inclusions in Fréchet spaces
    • DOI 10.1016/j.na.2004.12.002, PII S0362546X04005681
    • M. Benchohra, and A. Ouahab Controllability results for functional semilinear differential inclusions in Fréchet spaces Nonlinear Anal. 61 2005 405 423 (Pubitemid 40274753)
    • (2005) Nonlinear Analysis, Theory, Methods and Applications , vol.61 , Issue.3 , pp. 405-423
    • Benchohra, M.1    Ouahab, A.2
  • 33
    • 70350155256 scopus 로고    scopus 로고
    • Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces
    • Y.K. Chang, J.J. Nieto, and W.S. Li Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces J. Optim. Theory Appl. 142 2009 267 273
    • (2009) J. Optim. Theory Appl. , vol.142 , pp. 267-273
    • Chang, Y.K.1    Nieto, J.J.2    Li, W.S.3
  • 34
    • 68749106983 scopus 로고    scopus 로고
    • Controllability of fractional integrodifferential systems in Banach spaces
    • K. Balachandran, and J.Y. Park Controllability of fractional integrodifferential systems in Banach spaces Nonlinear Anal.: Hybrid Syst. 3 4 2009 363 367
    • (2009) Nonlinear Anal.: Hybrid Syst. , vol.3 , Issue.4 , pp. 363-367
    • Balachandran, K.1    Park, J.Y.2
  • 35
    • 58149196822 scopus 로고    scopus 로고
    • Existence results for fractional functional differential inclusions with infinite delay and application to control theory
    • M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional functional differential inclusions with infinite delay and application to control theory Fract. Calc. Appl. Anal. 11 2008 35 56
    • (2008) Fract. Calc. Appl. Anal. , vol.11 , pp. 35-56
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 36
    • 33745698037 scopus 로고    scopus 로고
    • Robust controllability of interval fractional order linear time invariant systems
    • Y.Q. Chen, H.S. Ahu, and D. Xue Robust controllability of interval fractional order linear time invariant systems Signal Process. 86 2006 2794 2802
    • (2006) Signal Process. , vol.86 , pp. 2794-2802
    • Chen, Y.Q.1    Ahu, H.S.2    Xue, D.3
  • 37
    • 68749108944 scopus 로고    scopus 로고
    • Controllability and observability for fractional control systems
    • A.B. Shamardan, and M.R.A. Moubarak Controllability and observability for fractional control systems J. Fract. Calc. 15 1999 25 34
    • (1999) J. Fract. Calc. , vol.15 , pp. 25-34
    • Shamardan, A.B.1    Moubarak, M.R.A.2
  • 38
    • 33747807905 scopus 로고    scopus 로고
    • Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay
    • DOI 10.1016/j.jmaa.2005.10.015, PII S0022247X05010516
    • A. Ouahab Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay J. Math. Anal. Appl. 323 2006 456 472 (Pubitemid 44276147)
    • (2006) Journal of Mathematical Analysis and Applications , vol.323 , Issue.1 , pp. 456-472
    • Ouahab, A.1
  • 39
    • 44349111167 scopus 로고    scopus 로고
    • Perturbed functional and neutral functional evolution equations with infinite delay in Fréchet spaces
    • S. Baghli, and M. Benchohra Perturbed functional and neutral functional evolution equations with infinite delay in Fréchet spaces Electron. J. Diff. Equ. 69 2008 1 19
    • (2008) Electron. J. Diff. Equ. , vol.69 , pp. 1-19
    • Baghli, S.1    Benchohra, M.2
  • 40
    • 77956953468 scopus 로고    scopus 로고
    • Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay
    • S. Baghli, and M. Benchohra Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay Differential Integral Equations 23 12 2010 31 50
    • (2010) Differential Integral Equations , vol.23 , Issue.12 , pp. 31-50
    • Baghli, S.1    Benchohra, M.2
  • 41
    • 70449534777 scopus 로고    scopus 로고
    • Controllability for semilinear functional and neutral functional evolution equations with infinite delay in Fréchet spaces
    • R.P. Agarwal, S. Baghli, and M. Benchohra Controllability for semilinear functional and neutral functional evolution equations with infinite delay in Fréchet spaces Appl. Math. Optim. 60 2009 253 274
    • (2009) Appl. Math. Optim. , vol.60 , pp. 253-274
    • Agarwal, R.P.1    Baghli, S.2    Benchohra, M.3
  • 42
    • 0002513583 scopus 로고
    • Phase space for retarded equations with infinite dealy
    • J. Hale, and J. Kato Phase space for retarded equations with infinite dealy Funkcial. Ekvac. 21 1978 11 41
    • (1978) Funkcial. Ekvac. , vol.21 , pp. 11-41
    • Hale, J.1    Kato, J.2
  • 43
    • 0004034109 scopus 로고
    • Functional Differential Equations with Unbounded Delay
    • Springer-Verlag Berlin
    • Y. Hino, S. Murukami, and T. Naito Functional Differential Equations with Unbounded Delay Lecture Notes in Mathematics vol. 1473 1991 Springer-Verlag Berlin
    • (1991) Lecture Notes in Mathematics , vol.1473
    • Hino, Y.1    Murukami, S.2    Naito, T.3
  • 44
    • 0011880971 scopus 로고    scopus 로고
    • Resultats de type LeraySchauder pour des contractions sur des espaces de Fréchet
    • M. Frigon, and A. Granas Resultats de type LeraySchauder pour des contractions sur des espaces de Fréchet Ann. Sci. Math. Quebec 22 1998 161 168
    • (1998) Ann. Sci. Math. Quebec , vol.22 , pp. 161-168
    • Frigon, M.1    Granas, A.2
  • 45
    • 0021578411 scopus 로고
    • Approach to nonlinear control problems using the fixed point methods, degree theory and pseudo-inverses
    • M.D. Quinn, and N. Carmichael An approach to nonlinear control problems using the fixed point methods, degree theory and pseudo-inverses Numer. Funct. Anal. Optim. 7 19841985 197 219 (Pubitemid 15458962)
    • (1984) Numerical Functional Analysis and Optimization , vol.7 , Issue.2-3 , pp. 197-219
    • Quinn, M.D.1    Carmichael, N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.