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Volumn 156, Issue 1, 2013, Pages 79-95

Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators

Author keywords

Characteristic solution operators; Controllability; Fractional derivative; Functional evolution equations; Sobolev

Indexed keywords

BANACH SPACES; DIFFERENTIAL EQUATIONS; FIXED POINT ARITHMETIC; FUNCTIONAL ANALYSIS; SOBOLEV SPACES;

EID: 84873992909     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-012-0174-7     Document Type: Article
Times cited : (131)

References (30)
  • 6
    • 0036680930 scopus 로고    scopus 로고
    • Some probability densities and fundamental solutions of fractional evolution equations
    • El-Borai, M. M.: Some probability densities and fundamental solutions of fractional evolution equations. Chaos Solitons Fractals 14, 433-440 (2002).
    • (2002) Chaos Solitons Fractals , vol.14 , pp. 433-440
    • El-Borai, M.M.1
  • 7
    • 34547561589 scopus 로고    scopus 로고
    • The fundamental solutions for fractional evolution equations of parabolic type
    • El-Borai, M. M.: The fundamental solutions for fractional evolution equations of parabolic type. J. Appl. Math. Stoch. Anal. 3, 197-211 (2004).
    • (2004) J. Appl. Math. Stoch. Anal. , vol.3 , pp. 197-211
    • El-Borai, M.M.1
  • 8
    • 68749106983 scopus 로고    scopus 로고
    • Controllability of fractional integrodifferential systems in Banach spaces
    • Balachandran, K., Park, J. Y.: Controllability of fractional integrodifferential systems in Banach spaces. Nonlinear Anal. Hybrid Syst. 3, 363-367 (2009).
    • (2009) Nonlinear Anal. Hybrid Syst. , vol.3 , pp. 363-367
    • Balachandran, K.1    Park, J.Y.2
  • 9
    • 74149093181 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional neutral evolution equations
    • Zhou, Y., Jiao, F.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59, 1063-1077 (2010).
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1063-1077
    • Zhou, Y.1    Jiao, F.2
  • 10
    • 77955515765 scopus 로고    scopus 로고
    • Nonlocal Cauchy problem for fractional evolution equations
    • Zhou, Y., Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal., Real World Appl. 11, 4465-4475 (2010).
    • (2010) Nonlinear Anal., Real World Appl. , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 11
    • 77956176473 scopus 로고    scopus 로고
    • On recent developments in the theory of abstract differential equations with fractional derivatives
    • Hernández, E., O'Regan, D., Balachandran, K.: On recent developments in the theory of abstract differential equations with fractional derivatives. Nonlinear Anal., Theory Methods Appl. 73, 3462-3471 (2010).
    • (2010) Nonlinear Anal., Theory Methods Appl. , vol.73 , pp. 3462-3471
    • Hernández, E.1    O'Regan, D.2    Balachandran, K.3
  • 12
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • Wang, J., Zhou, Y.: A class of fractional evolution equations and optimal controls. Nonlinear Anal., Real World Appl. 12, 262-272 (2011).
    • (2011) Nonlinear Anal., Real World Appl. , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 13
    • 80052035803 scopus 로고    scopus 로고
    • Existence and controllability results for fractional semilinear differential inclusions
    • Wang, J., Zhou, Y.: Existence and controllability results for fractional semilinear differential inclusions. Nonlinear Anal., Real World Appl. 12, 3642-3653 (2011).
    • (2011) Nonlinear Anal., Real World Appl. , vol.12 , pp. 3642-3653
    • Wang, J.1    Zhou, Y.2
  • 14
    • 80051576826 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional control systems in Banach spaces
    • Wang, J., Zhou, Y.: Analysis of nonlinear fractional control systems in Banach spaces. Nonlinear Anal., Theory Methods Appl. 74, 5929-5942 (2011).
    • (2011) Nonlinear Anal., Theory Methods Appl. , vol.74 , pp. 5929-5942
    • Wang, J.1    Zhou, Y.2
  • 15
    • 79960988377 scopus 로고    scopus 로고
    • On the approximate controllability of semilinear fractional differential systems
    • Sakthivel, R., Ren, Y., Mahmudov, N. I.: On the approximate controllability of semilinear fractional differential systems. Comput. Math. Appl. 62, 1451-1459 (2011).
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1451-1459
    • Sakthivel, R.1    Ren, Y.2    Mahmudov, N.I.3
  • 16
    • 79960984881 scopus 로고    scopus 로고
    • Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems
    • Debbouchea, A., Baleanu, D.: Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl. 62, 1442-1450 (2011).
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1442-1450
    • Debbouchea, A.1    Baleanu, D.2
  • 17
    • 84855519663 scopus 로고    scopus 로고
    • On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay
    • Wang, J., Zhou, Y., Medved', M.: On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay. J. Optim. Theory Appl. 152, 31-50 (2012).
    • (2012) J. Optim. Theory Appl. , vol.152 , pp. 31-50
    • Wang, J.1    Zhou, Y.2    Medved', M.3
  • 18
    • 84855992801 scopus 로고    scopus 로고
    • Mittag-Leffer-Ulam stabilities of fractional evolution equations
    • Wang, J., Zhou, Y.: Mittag-Leffer-Ulam stabilities of fractional evolution equations. Appl. Math. Lett. 25, 723-728 (2012).
    • (2012) Appl. Math. Lett. , vol.25 , pp. 723-728
    • Wang, J.1    Zhou, Y.2
  • 19
    • 84862777911 scopus 로고    scopus 로고
    • Optimal feedback control for semilinear fractional evolution equations in Banach spaces
    • Wang, J., Zhou, Y., Wei, W.: Optimal feedback control for semilinear fractional evolution equations in Banach spaces. Syst. Control Lett. 61, 472-476 (2012).
    • (2012) Syst. Control Lett. , vol.61 , pp. 472-476
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 20
    • 84862793261 scopus 로고    scopus 로고
    • Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces
    • Wang, J., Fan, Z., Zhou, Y.: Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces. J. Optim. Theory Appl. 154, 292-302 (2012).
    • (2012) J. Optim. Theory Appl. , vol.154 , pp. 292-302
    • Wang, J.1    Fan, Z.2    Zhou, Y.3
  • 21
    • 84862787593 scopus 로고    scopus 로고
    • Complete controllability of fractional evolution systems
    • Wang, J., Zhou, Y.: Complete controllability of fractional evolution systems. Commun. Nonlinear Sci. Numer. Simul. 17, 4346-4355 (2012).
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 4346-4355
    • Wang, J.1    Zhou, Y.2
  • 22
    • 84861937080 scopus 로고    scopus 로고
    • Fractional Schrödinger equations with potential and optimal controls
    • Wang, J., Zhou, Y., Wei, W.: Fractional Schrödinger equations with potential and optimal controls. Nonlinear Anal., Real World Appl. 13, 2755-2766 (2012).
    • (2012) Nonlinear Anal., Real World Appl. , vol.13 , pp. 2755-2766
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 23
    • 80054110209 scopus 로고    scopus 로고
    • Abstract fractional Cauchy problems with almost sectorial operators
    • Wang, R. N., Chen, D. H., Xiao, T. J.: Abstract fractional Cauchy problems with almost sectorial operators. J. Differ. Equs. 252, 202-235 (2012).
    • (2012) J. Differ. Equs. , vol.252 , pp. 202-235
    • Wang, R.N.1    Chen, D.H.2    Xiao, T.J.3
  • 24
    • 84862828893 scopus 로고    scopus 로고
    • Approximate controllability of fractional order semilinear systems with bounded delay
    • Kumar, S., Sukavanam, N.: Approximate controllability of fractional order semilinear systems with bounded delay. J. Differ. Equs. 252, 6163-6174 (2012).
    • (2012) J. Differ. Equs. , vol.252 , pp. 6163-6174
    • Kumar, S.1    Sukavanam, N.2
  • 25
    • 84861344017 scopus 로고    scopus 로고
    • Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
    • Li, K., Peng, J., Jia, J.: Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives. J. Funct. Anal. 263, 476-510 (2012).
    • (2012) J. Funct. Anal. , vol.263 , pp. 476-510
    • Li, K.1    Peng, J.2    Jia, J.3
  • 26
    • 0039491570 scopus 로고    scopus 로고
    • Controllability of functional differential systems of Sobolev type in Banach spaces
    • Balachandran, K., Dauer, J. P.: Controllability of functional differential systems of Sobolev type in Banach spaces. Kybernetika 34, 349-357 (1998).
    • (1998) Kybernetika , vol.34 , pp. 349-357
    • Balachandran, K.1    Dauer, J.P.2
  • 27
    • 84862801986 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions
    • Li, F., Liang, J., Xu, H. K.: Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions. J. Math. Anal. Appl. 391, 510-525 (2012).
    • (2012) J. Math. Anal. Appl. , vol.391 , pp. 510-525
    • Li, F.1    Liang, J.2    Xu, H.K.3
  • 28
    • 0020750901 scopus 로고
    • A partial functional differential equation of Sobolev type
    • Lightbourne, J. H., Rankin, S. M.: A partial functional differential equation of Sobolev type. J. Math. Anal. Appl. 93, 328-337 (1983).
    • (1983) J. Math. Anal. Appl. , vol.93 , pp. 328-337
    • Lightbourne, J.H.1    Rankin, S.M.2
  • 29
    • 23844530956 scopus 로고    scopus 로고
    • β) and I(t): application to the Mittag-Leffler and asymptotic inverse power law relaxation functions
    • β) and I(t): application to the Mittag-Leffler and asymptotic inverse power law relaxation functions. J. Math. Chem. 38, 265-270 (2005).
    • (2005) J. Math. Chem. , vol.38 , pp. 265-270
    • Berberan-Santos, M.N.1
  • 30
    • 34147096761 scopus 로고    scopus 로고
    • Properties of the Mittag-Leffler relaxation function
    • Berberan-Santos, M. N.: Properties of the Mittag-Leffler relaxation function. J. Math. Chem. 38, 629-635 (2005).
    • (2005) J. Math. Chem. , vol.38 , pp. 629-635
    • Berberan-Santos, M.N.1


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