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Volumn 2012, Issue , 2012, Pages

Nonlocal nonlinear integrodifferential equations of fractional orders

Author keywords

Fractional evolution equation; Nonlocal condition; Schauder's fixed point theorem; Uniformly continuous semigroup

Indexed keywords


EID: 84866647774     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1186/1687-2770-2012-78     Document Type: Article
Times cited : (61)

References (31)
  • 1
    • 73249139676 scopus 로고    scopus 로고
    • On the concept of solution for fractional differential equations with uncertainty
    • Agarwal, RP, Lakshmikanthama, V, Nieto, JJ: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859-2862 (2010)
    • (2010) Nonlinear Anal. , vol.72 , pp. 2859-2862
    • Agarwal, R.P.1    Lakshmikanthama, V.2    Nieto, J.J.3
  • 2
    • 68949086378 scopus 로고    scopus 로고
    • Existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations
    • Article ID 494720 (2009)
    • Ahmad, B, Nieto, JJ: Existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations. Abstr. Appl. Anal. 2009, Article ID 494720 (2009)
    • (2009) Abstr. Appl. Anal.
    • Ahmad, B.1    Nieto, J.J.2
  • 3
    • 0043190843 scopus 로고    scopus 로고
    • Existence of solutions of nonlinear integrodifferential equations of sobolev type with nonlocal condition in banach spaces
    • Balachandran, K, Uchiyama, K: Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces. Proc. Indian Acad. Sci. Math. Sci. 110(2), 225-232 (2000)
    • (2000) Proc. Indian Acad. Sci. Math. Sci. , vol.110 , Issue.2 , pp. 225-232
    • Balachandran, K.1    Uchiyama, K.2
  • 4
    • 58249109762 scopus 로고    scopus 로고
    • Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions
    • Balachandran, K, Samuel, FP: Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions. Electron. J. Differ. Equ. 2009(6), 1-7 (2009)
    • (2009) Electron. J. Differ. Equ. , vol.2009 , Issue.6 , pp. 1-7
    • Balachandran, K.1    Samuel, F.P.2
  • 5
    • 33845982561 scopus 로고    scopus 로고
    • Existence of solutions of integrodifferential evolution equations with time varying delays
    • Balachandran, K, Kumar, RR: Existence of solutions of integrodifferential evolution equations with time varying delays. Appl. Math. E-Notes 7, 1-8 (2007)
    • (2007) Appl. Math. E-notes , vol.7 , pp. 1-8
    • Balachandran, K.1    Kumar, R.R.2
  • 6
    • 76649111047 scopus 로고    scopus 로고
    • On the global existence of solutions to a class of fractional differential equations
    • Baleanu, D, Mustafa, OG: On the global existence of solutions to a class of fractional differential equations. Comput. Math. Appl. 59(5), 1835-1841 (2010)
    • (2010) Comput. Math. Appl. , vol.59 , Issue.5 , pp. 1835-1841
    • Baleanu, D.1    Mustafa, O.G.2
  • 7
    • 79251613813 scopus 로고    scopus 로고
    • Asymptotically linear solutions for some linear fractional differential equations
    • Article ID 865139 (2010)
    • Baleanu, D, Mustafa, OG, Agarwal, RP: Asymptotically linear solutions for some linear fractional differential equations. Abstr. Appl. Anal. 2010, Article ID 865139 (2010)
    • (2010) Abstr. Appl. Anal.
    • Baleanu, D.1    Mustafa, O.G.2    Agarwal, R.P.3
  • 8
    • 71649091559 scopus 로고    scopus 로고
    • Existence results for fractional order semilinear functional differential equations with nondense domain
    • Belmekki, M, Benchohra, M: Existence results for fractional order semilinear functional differential equations with nondense domain. Nonlinear Anal. 72, 925-932 (2010)
    • (2010) Nonlinear Anal. , vol.72 , pp. 925-932
    • Belmekki, M.1    Benchohra, M.2
  • 9
    • 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. 162, 494-505 (1991)
    • (1991) J. Math. Anal. Appl. , vol.162 , pp. 494-505
    • Byszewski, L.1
  • 10
    • 0032165473 scopus 로고    scopus 로고
    • Application of properties of the right-hand sides of evolution equations to an investigation of nonlocal evolution problems
    • PII S0362546X97005944
    • Byszewski, L: Applications of properties of the right hand sides of evolution equations to an investigation of nonlocal evolution problems. Nonlinear Anal. 33, 413-426 (1998) (Pubitemid 128446682)
    • (1998) Nonlinear Analysis, Theory, Methods and Applications , vol.33 , Issue.5 , pp. 413-426
    • Byszewski, L.1
  • 11
    • 79960984881 scopus 로고    scopus 로고
    • Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems
    • Debbouche, 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
    • Debbouche, A.1    Baleanu, D.2
  • 12
    • 84866702355 scopus 로고    scopus 로고
    • Fractional nonlocal impulsive quasilinear multi-delay integro-differential systems
    • Debbouche, A: Fractional nonlocal impulsive quasilinear multi-delay integro-differential systems. Adv. Differ. Equ. 5, 1-10 (2011)
    • (2011) Adv. Differ. Equ. , vol.5 , pp. 1-10
    • Debbouche, A.1
  • 13
    • 79960994486 scopus 로고    scopus 로고
    • Fractional evolution integro-differential systems with nonlocal conditions
    • Debbouche, A: Fractional evolution integro-differential systems with nonlocal conditions. Adv. Dyn. Syst. Appl. 5(1), 49-60 (2010)
    • (2010) Adv. Dyn. Syst. Appl. , vol.5 , Issue.1 , pp. 49-60
    • Debbouche, A.1
  • 14
    • 65749094471 scopus 로고    scopus 로고
    • Weak almost periodic and optimal mild solutions of fractional evolution equations
    • Debbouche, A, El-Borai, MM: Weak almost periodic and optimal mild solutions of fractional evolution equations. Electron. J. Differ. Equ. 2009(46), 1-8 (2009)
    • (2009) Electron. J. Differ. Equ. , vol.2009 , Issue.46 , pp. 1-8
    • Debbouche, A.1    El-Borai, M.M.2
  • 15
    • 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. 179, 630-637 (1993)
    • (1993) J. Math. Anal. Appl. , vol.179 , pp. 630-637
    • Deng, K.1
  • 16
    • 77956742449 scopus 로고    scopus 로고
    • On some fractional integro-differential equations with analytic semigroups
    • El-Borai, MM, Debbouche, A: On some fractional integro-differential equations with analytic semigroups. Int. J. Contemp. Math. Sci. 4(28), 1361-1371 (2009)
    • (2009) Int. J. Contemp. Math. Sci. , vol.4 , Issue.28 , pp. 1361-1371
    • El-Borai, M.M.1    Debbouche, A.2
  • 17
    • 0036680930 scopus 로고    scopus 로고
    • Some probability densities and fundamental solutions of fractional evolution equations
    • DOI 10.1016/S0960-0779(01)00208-9, PII S0960077901002089
    • El-Borai, MM: Some probability densities and fundamental solutions of fractional evolution equations. Chaos Solitons Fractals 14(3), 433-440 (2002) (Pubitemid 34182465)
    • (2002) Chaos, Solitons and Fractals , vol.14 , Issue.3 , pp. 433-440
    • El-Borai, M.M.1
  • 18
    • 0345867025 scopus 로고    scopus 로고
    • Semigroups and some nonlinear fractional differential equations
    • El-Borai, MM: Semigroups and some nonlinear fractional differential equations. Appl. Math. Comput. 149(3), 823-831 (2004)
    • (2004) Appl. Math. Comput. , vol.149 , Issue.3 , pp. 823-831
    • El-Borai, M.M.1
  • 19
    • 65749091514 scopus 로고    scopus 로고
    • On some fractional evolution equations with nonlocal conditions
    • El-Borai, MM: On some fractional evolution equations with nonlocal conditions. Int. J. Pure Appl. Math. 24(3), 405-413 (2005)
    • (2005) Int. J. Pure Appl. Math. , vol.24 , Issue.3 , pp. 405-413
    • El-Borai, M.M.1
  • 21
    • 79955006527 scopus 로고    scopus 로고
    • Mild solutions for fractional differential equations with nonlocal conditions
    • Article ID 287861
    • Li, F: Mild solutions for fractional differential equations with nonlocal conditions. Adv. Differ. Equ. 2010, Article ID 287861 (2010)
    • (2010) Adv. Differ. Equ. , vol.2010
    • Li, F.1
  • 22
    • 0030651602 scopus 로고    scopus 로고
    • Analysis and design of fractional-order digital control systems
    • Machado, JAT: Analysis and design of fractional-order digital control systems. Syst. Anal. Model. Simul. 27(2-3), 107-122 (1997)
    • (1997) Syst. Anal. Model. Simul. , vol.27 , Issue.2-3 , pp. 107-122
    • Machado, J.A.T.1
  • 23
    • 59249101044 scopus 로고    scopus 로고
    • Mild solutions for semilinear fractional differential equations
    • Mophou, GM, N'Guerekata, GM: Mild solutions for semilinear fractional differential equations. Electron. J. Differ. Equ. 2009(21), 1-9 (2009)
    • (2009) Electron. J. Differ. Equ. , vol.2009 , Issue.21 , pp. 1-9
    • Mophou, G.M.1    N'Guerekata, G.M.2
  • 24
    • 0003244044 scopus 로고    scopus 로고
    • Fractional differential equations
    • Academic Press, San Diego
    • Podlubny, I: Fractional Differential Equations. Math Science and Eng., vol. 198. Academic Press, San Diego (1999)
    • (1999) Math Science and Eng. , vol.198
    • Podlubny, I.1
  • 25
    • 73249114916 scopus 로고    scopus 로고
    • On a boundary controller of fractional type
    • Tatar, N-E: On a boundary controller of fractional type. Nonlinear Anal. 72, 3209-3215 (2010)
    • (2010) Nonlinear Anal. , vol.72 , pp. 3209-3215
    • Tatar, N.-E.1
  • 27
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • Wang, JR, 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.R.1    Zhou, Y.2
  • 28
    • 84555190950 scopus 로고    scopus 로고
    • Controllability of semilinear integrodifferential systems with nonlocal conditions
    • Yan, Z: Controllability of semilinear integrodifferential systems with nonlocal conditions. Int. J. Comput. Appl. Math. 3(2), 221-236 (2007)
    • (2007) Int. J. Comput. Appl. Math. , vol.3 , Issue.2 , pp. 221-236
    • Yan, Z.1
  • 30
    • 79952151650 scopus 로고    scopus 로고
    • Positive solutions to boundary value problems of nonlinear fractional differential equations
    • Article ID 390543
    • Zhao, Y, Sun, S, Han, Z, Li, Q: Positive solutions to boundary value problems of nonlinear fractional differential equations. Abstr. Appl. Anal. 2011, Article ID 390543 (2011)
    • (2011) Abstr. Appl. Anal. , vol.2011
    • Zhao, Y.1    Sun, S.2    Han, Z.3    Li, Q.4
  • 31
    • 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


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