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Volumn 12, Issue 6, 2014, Pages 911-922

On the nonlocal Cauchy problem for semilinear fractional order evolution equations

Author keywords

Existence; Fractional order evolution equations; Mild solution; Nonlocal Cauchy problem

Indexed keywords


EID: 84896549735     PISSN: 18951074     EISSN: 16443616     Source Type: Journal    
DOI: 10.2478/s11533-013-0381-y     Document Type: Article
Times cited : (34)

References (37)
  • 2
    • 58049141923 scopus 로고    scopus 로고
    • On the nonlocal initial value problem for first order differential equations
    • Boucherif A., Precup R., On the nonlocal initial value problem for first order differential equations, Fixed Point Theory, 2003, 4(2), 205-212.
    • (2003) Fixed Point Theory , vol.4 , Issue.2 , pp. 205-212
    • Boucherif, A.1    Precup, R.2
  • 3
    • 67349249408 scopus 로고    scopus 로고
    • Semilinear evolution equations with nonlocal initial conditions
    • Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507-516.
    • (2007) Dynam. Systems Appl. , vol.16 , Issue.3 , pp. 507-516
    • Boucherif, A.1    Precup, R.2
  • 4
    • 29844435933 scopus 로고    scopus 로고
    • Controllability of semilinear boundary problems with nonlocal initial conditions
    • Boulite S., Idrissi A., Maniar L., Controllability of semilinear boundary problems with nonlocal initial conditions, J. Math. Anal. Appl., 2006, 316(2), 566-578.
    • (2006) J. Math. Anal. Appl. , vol.316 , Issue.2 , pp. 566-578
    • Boulite, S.1    Idrissi, A.2    Maniar, L.3
  • 5
    • 44949272606 scopus 로고
    • Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
    • Byszewski L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 1991, 162(2), 494-505.
    • (1991) J. Math. Anal. Appl. , vol.162 , Issue.2 , pp. 494-505
    • Byszewski, L.1
  • 6
    • 84948514180 scopus 로고
    • Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space
    • Byszewski L., Lakshmikantham V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 1991, 40(1), 11-19.
    • (1991) Appl. Anal. , vol.40 , Issue.1 , pp. 11-19
    • Byszewski, L.1    Lakshmikantham, V.2
  • 7
    • 60349098158 scopus 로고    scopus 로고
    • On impulsive hyperbolic differential inclusions with nonlocal initial conditions
    • Chang Y.-K., Nieto J. J., Li W.-S., On impulsive hyperbolic differential inclusions with nonlocal initial conditions, J. Optim. Theory Appl., 2009, 140(3), 431-442.
    • (2009) J. Optim. Theory Appl. , vol.140 , Issue.3 , pp. 431-442
    • Chang, Y.-K.1    Nieto, J.J.2    Li, W.-S.3
  • 8
    • 0000297319 scopus 로고
    • Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions
    • Deng K., Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl., 1993, 179(2), 630-637.
    • (1993) J. Math. Anal. Appl. , vol.179 , Issue.2 , pp. 630-637
    • Deng, K.1
  • 10
    • 84856219740 scopus 로고    scopus 로고
    • On nonlocal problems for fractional differential equations in Banach spaces
    • Dong X., Wang J., Zhou Y., On nonlocal problems for fractional differential equations in Banach spaces, Opuscula Math., 2011, 31(3), 341-357.
    • (2011) Opuscula Math. , vol.31 , Issue.3 , pp. 341-357
    • Dong, X.1    Wang, J.2    Zhou, Y.3
  • 11
    • 71649105460 scopus 로고    scopus 로고
    • Impulsive problems for semilinear differential equations with nonlocal conditions
    • Fan Z., Impulsive problems for semilinear differential equations with nonlocal conditions, Nonlinear Anal., 2010, 72(2), 1104-1109.
    • (2010) Nonlinear Anal. , vol.72 , Issue.2 , pp. 1104-1109
    • Fan, Z.1
  • 12
    • 70450222292 scopus 로고    scopus 로고
    • Existence results for semilinear differential equations with nonlocal and impulsive conditions
    • Fan Z., Li G., Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 2010, 258(5), 1709-1727.
    • (2010) J. Funct. Anal. , vol.258 , Issue.5 , pp. 1709-1727
    • Fan, Z.1    Li, G.2
  • 13
    • 0038137295 scopus 로고    scopus 로고
    • Existence of solutions for neutral functional differential evolution equations with nonlocal conditions
    • Fu X., Ezzinbi K., Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Anal., 2003, 54(2), 215-227.
    • (2003) Nonlinear Anal. , vol.54 , Issue.2 , pp. 215-227
    • Fu, X.1    Ezzinbi, K.2
  • 14
    • 38249006923 scopus 로고
    • Existence and uniqueness of solutions to semilinear nonlocal parabolic equations
    • Jackson D., Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Anal. Appl., 1993, 172(1), 256-265.
    • (1993) J. Math. Anal. Appl. , vol.172 , Issue.1 , pp. 256-265
    • Jackson, D.1
  • 17
    • 2342582717 scopus 로고
    • Nonlocal Cauchy problems governed by compact operator families
    • Liang J., Liu J., Xiao T.-J., Nonlocal Cauchy problems governed by compact operator families, Nonlinear Anal. TMA, 1994, 57(2), 183-189.
    • (1994) Nonlinear Anal. TMA , vol.57 , Issue.2 , pp. 183-189
    • Liang, J.1    Liu, J.2    Xiao, T.-J.3
  • 18
    • 61549131656 scopus 로고    scopus 로고
    • Existence for a class of partial differential equations with nonlocal conditions
    • Liu H., Chang J.-C., Existence for a class of partial differential equations with nonlocal conditions, Nonlinear Anal., 2009, 70(9), 3076-3083.
    • (2009) Nonlinear Anal. , vol.70 , Issue.9 , pp. 3076-3083
    • Liu, H.1    Chang, J.-C.2
  • 21
    • 58149231350 scopus 로고    scopus 로고
    • A Cauchy problem for some fractional differential abstract differential equation with non local conditions
    • N'Guérékata G. M., A Cauchy problem for some fractional differential abstract differential equation with non local conditions, Nonlinear Anal., 2009, 70(5), 1873-1876.
    • (2009) Nonlinear Anal. , vol.70 , Issue.5 , pp. 1873-1876
    • N'Guérékata, G.M.1
  • 22
    • 84883131048 scopus 로고    scopus 로고
    • Corrigendum: A Cauchy problem for some fractional differential equations
    • N'Guérékata G. M., Corrigendum: A Cauchy problem for some fractional differential equations, Commun. Math. Anal., 2009, 7(1), 11.
    • (2009) Commun. Math. Anal. , vol.7 , Issue.1 , pp. 11
    • N'Guérékata, G.M.1
  • 23
    • 84863499018 scopus 로고    scopus 로고
    • Initial value problems for first-order differential systems with general nonlocal conditions
    • #74
    • Nica O., Initial value problems for first-order differential systems with general nonlocal conditions, Electron. J. Differential Equations, 2012, #74.
    • (2012) Electron. J. Differential Equations
    • Nica, O.1
  • 24
    • 84871273185 scopus 로고    scopus 로고
    • On the nonlocal initial value problem for first order differential systems
    • Nica O., Precup R., On the nonlocal initial value problem for first order differential systems, Stud. Univ. Babe?-Bolyai Math., 2001, 56(3), 113-125.
    • (2001) Stud. Univ. Babe?-Bolyai Math. , vol.56 , Issue.3 , pp. 113-125
    • Nica, O.1    Precup, R.2
  • 25
    • 0031153492 scopus 로고    scopus 로고
    • Global existence for semilinear evolution equations with nonlocal conditions
    • Ntouyas S. K., Tsamatos P. Ch., Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl., 1997, 210(2), 679-687.
    • (1997) J. Math. Anal. Appl. , vol.210 , Issue.2 , pp. 679-687
    • Ntouyas, S.K.1    Tsamatos, P.C.2
  • 26
    • 0001775771 scopus 로고    scopus 로고
    • Fixed-point theory for the sum of two operators
    • O'Regan D., Fixed-point theory for the sum of two operators, Appl. Math. Lett., 1996, 9(1), 1-8.
    • (1996) Appl. Math. Lett. , vol.9 , Issue.1 , pp. 1-8
    • O'Regan, D.1
  • 28
    • 0003838373 scopus 로고
    • Cambridge Tracts in Math, London-New York: Cambridge University Press
    • Smart D. R., Fixed Point Theorems, Cambridge Tracts in Math., 66, Cambridge University Press, London-New York, 1974.
    • (1974) Fixed Point Theorems , vol.66
    • Smart, D.R.1
  • 30
    • 78249274535 scopus 로고    scopus 로고
    • Existence results for an evolution problem with fractional nonlocal conditions
    • Tatar N., Existence results for an evolution problem with fractional nonlocal conditions, Comput. Math. Appl., 2010, 60(11), 2971-2982.
    • (2010) Comput. Math. Appl. , vol.60 , Issue.11 , pp. 2971-2982
    • Tatar, N.1
  • 31
    • 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., 2011, 12(1), 262-272.
    • (2011) Nonlinear Anal. Real World Appl. , vol.12 , Issue.1 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 32
    • 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., 2011, 74(17), 5929-5942.
    • (2011) Nonlinear Anal. , vol.74 , Issue.17 , pp. 5929-5942
    • Wang, J.1    Zhou, Y.2
  • 33
    • 85088180734 scopus 로고    scopus 로고
    • Alternative results and robustness for fractional evolution equations with periodic boundary conditions
    • Wang J., Zhou Y., Fečkan M., Alternative results and robustness for fractional evolution equations with periodic boundary conditions, Electron. J. Qual. Theory Diff. Equ., 2011, #97.
    • (2011) Electron. J. Qual. Theory Diff. Equ. , pp. 97
    • Wang, J.1    Zhou, Y.2    Fečkan, M.3
  • 34
    • 84885366423 scopus 로고    scopus 로고
    • Abstract Cauchy problem for fractional differential equations
    • Wang J., Zhou Y., Fečkan M., Abstract Cauchy problem for fractional differential equations, Nonlinear Dynam., 2013, 71(4), 685-700.
    • (2013) Nonlinear Dynam. , vol.71 , Issue.4 , pp. 685-700
    • Wang, J.1    Zhou, Y.2    Fečkan, M.3
  • 35
    • 26944502327 scopus 로고    scopus 로고
    • Nonlinear differential equations with nonlocal conditions in Banach spaces
    • Xue X., Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Anal., 2005, 63(4), 575-586.
    • (2005) Nonlinear Anal. , vol.63 , Issue.4 , pp. 575-586
    • Xue, X.1
  • 36
    • 77955515765 scopus 로고    scopus 로고
    • Nonlocal Cauchy problem for fractional evolution equations
    • Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465-4475.
    • (2010) Nonlinar Anal. Real World Appl. , vol.11 , Issue.5 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 37
    • 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., 2010, 59(3), 1063-1077.
    • (2010) Comput. Math. Appl. , vol.59 , Issue.3 , pp. 1063-1077
    • Zhou, Y.1    Jiao, F.2


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