메뉴 건너뛰기




Volumn 8, Issue 4, 2011, Pages 345-361

On the new concept of solutions and existence results for impulsive fractional evolution equations

Author keywords

Caputo fractional derivative; Cauchy problems; Evolution equa tions; Impulsive conditions; Nonlocal problmes; PC mild solutions

Indexed keywords


EID: 84255168779     PISSN: 1548159X     EISSN: 21637873     Source Type: Journal    
DOI: 10.4310/dpde.2011.v8.n4.a3     Document Type: Article
Times cited : (246)

References (39)
  • 5
    • 63449090309 scopus 로고    scopus 로고
    • Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions
    • N. Abada, M. Benchohra, H. Hammouche, Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, J. Diff. Eqs., 246(2009), 3834-3863.
    • (2009) J. Diff. Eqs , vol.246 , pp. 3834-3863
    • Abada, N.1    Benchohra, M.2    Hammouche, H.3
  • 6
    • 1942509677 scopus 로고    scopus 로고
    • Existence of optimal controls for a general class of impulsive systems on Banach space
    • N. U. Ahmed, Existence of optimal controls for a general class of impulsive systems on Banach space, SIAM J. Control Optimal, 42(2003), 669-685.
    • (2003) SIAM J. Control Optimal , vol.42 , pp. 669-685
    • Ahmed, N.U.1
  • 7
    • 34249936153 scopus 로고    scopus 로고
    • Optimal feedback control for impulsive systems on the space of finitely additive measures
    • N. U. Ahmed, Optimal feedback control for impulsive systems on the space of finitely additive measures, Publ. Math. Debrecen, 70(2007), 371-393.
    • (2007) Publ. Math. Debrecen , vol.70 , pp. 371-393
    • Ahmed, N.U.1
  • 8
    • 10044282936 scopus 로고    scopus 로고
    • On the smoothness of solutions of impulsive autonomous systems
    • M. U. Akhmet, On the smoothness of solutions of impulsive autonomous systems, Nonlinear Anal.:TMA, 60(2005), 311-324.
    • (2005) Nonlinear Anal.:TMA , vol.60 , pp. 311-324
    • Akhmet, M.U.1
  • 9
    • 70450222292 scopus 로고    scopus 로고
    • Existence results for semilinear differential equations with nonlocal and impulsive conditions
    • Z. Fan, G. Li, Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 258(2010), 1709-1727.
    • (2010) J. Funct. Anal , vol.258 , pp. 1709-1727
    • Fan, Z.1    Li, G.2
  • 10
    • 71649105460 scopus 로고    scopus 로고
    • Impulsive problems for semilinear differential equations with nonlocal conditions
    • Z. Fan, Impulsive problems for semilinear differential equations with nonlocal conditions, Nonlinear Anal.: TMA, 72(2010), 1104-1109.
    • (2010) Nonlinear Anal.: TMA , vol.72 , pp. 1104-1109
    • Fan, Z.1
  • 11
    • 58049145638 scopus 로고    scopus 로고
    • Nonlocal impulsive problems for nonlinear differential equations in Banach spaces
    • J. Liang, J. H. Liu and T.-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Model., 49(2009), 798-804.
    • (2009) Math. Comput. Model , vol.49 , pp. 798-804
    • Liang, J.1    Liu, J.H.2    Xiao, T.-J.3
  • 12
    • 0003168187 scopus 로고    scopus 로고
    • Nonlinear impulsive evolution equations
    • J. Liu, Nonlinear impulsive evolution equations, Dyn. Contin. Discrete Impuls. Syst., 6(1999), 77-85.
    • (1999) Dyn. Contin. Discrete Impuls. Syst , vol.6 , pp. 77-85
    • Liu, J.1
  • 13
    • 0041726910 scopus 로고    scopus 로고
    • Chaos in singular impulsive O.D.E
    • F. Battelli, M. Fe ̌ckan, Chaos in singular impulsive O.D.E., Nonlinear Anal.:TMA, 28(1997), 655-671.
    • (1997) Nonlinear Anal.:TMA , vol.28 , pp. 655-671
    • Battelli, F.1    Fěckan, M.2
  • 14
    • 71549128004 scopus 로고    scopus 로고
    • Existence and uniqueness of mild solution to impulsive fractional differetial equations
    • G. M. Mophou, Existence and uniqueness of mild solution to impulsive fractional differetial equations, Nonlinear Anal.:TMA, 72(2010), 1604-1615.
    • (2010) Nonlinear Anal.:TMA , vol.72 , pp. 1604-1615
    • Mophou, G.M.1
  • 15
    • 56549095607 scopus 로고    scopus 로고
    • Variational approach to impulsive differential equations
    • J. J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Non- linear Anal.:RWA, 10(2009), 680-690.
    • (2009) Non- Linear Anal.:RWA , vol.10 , pp. 680-690
    • Nieto, J.J.1    O'Regan, D.2
  • 16
    • 72149098558 scopus 로고    scopus 로고
    • Periodic solutions of semilinear impulsive periodic system on Banach space
    • J. Wang, X. Xiang, Y. Peng, Periodic solutions of semilinear impulsive periodic system on Banach space, Nonlinear Anal.:TMA, 71(2009), e1344-e1353.
    • (2009) Nonlinear Anal.:TMA , vol.71
    • Wang, J.1    Xiang, X.2    Peng, Y.3
  • 17
    • 77957991525 scopus 로고    scopus 로고
    • A class of nonlocal impulsive problems for integrodifferential equations in Banach spaces
    • J. Wang, W. Wei, A class of nonlocal impulsive problems for integrodifferential equations in Banach spaces, Results Math., 58(2010), 379-397.
    • (2010) Results Math , vol.58 , pp. 379-397
    • Wang, J.1    Wei, W.2
  • 18
    • 33646451517 scopus 로고    scopus 로고
    • Nonlinear impulsive integro-differential equation of mixed type and optimal controls
    • W. Wei, X. Xiang, Y. Peng, Nonlinear impulsive integro-differential equation of mixed type and optimal controls, Optimization, 55(2006), 141-156.
    • (2006) Optimization , vol.55 , pp. 141-156
    • Wei, W.1    Xiang, X.2    Peng, Y.3
  • 19
    • 53849105289 scopus 로고    scopus 로고
    • On a class of strongly nonlinear impulsive differential equation with time delay
    • W. Wei, S. H. Hou, K. L. Teo, On a class of strongly nonlinear impulsive differential equation with time delay, Nonlinear Dyn. Syst. Theory, 6(2006), 281-293.
    • (2006) Nonlinear Dyn. Syst. Theory , vol.6 , pp. 281-293
    • Wei, W.1    Hou, S.H.2    Teo, K.L.3
  • 20
    • 77956153506 scopus 로고    scopus 로고
    • The analysis of fractional differential equations
    • K. Diethelm, The analysis of fractional differential equations, Lecture Notes in Mathematics, 2010.
    • (2010) Lecture Notes In Mathematics
    • Diethelm, K.1
  • 21
    • 77956684069 scopus 로고    scopus 로고
    • Theory and applications of fractional differential equations
    • Elsevier Science B.V., Amsterdam
    • A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
    • (2006) North-Holland Mathematics Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 26
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • R. P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math., 109(2010), 973-1033.
    • (2010) Acta. Appl. Math , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 27
    • 67650110018 scopus 로고    scopus 로고
    • A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
    • 2009), Article ID 981728
    • R. P. Agarwal, M. Belmekki, M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Difference Equ., 2009(2009), Article ID 981728, 47pp.
    • (2009) Adv. Difference Equ , pp. 47
    • Agarwal, R.P.1    Belmekki, M.2    Benchohra, M.3
  • 28
    • 0036680930 scopus 로고    scopus 로고
    • Some probability densities and fundamental solutions of fractional evolution equations
    • M. M. El-Borai, Some probability densities and fundamental solutions of fractional evolution equations, Chaos, Sol. Frac., 14(2002), 433-440.
    • (2002) Chaos, Sol. Frac , vol.14 , pp. 433-440
    • El-Borai, M.M.1
  • 29
    • 34547561589 scopus 로고    scopus 로고
    • The fundamental solutions for fractional evolution equations of parabolic type
    • M. M. El-Borai, The fundamental solutions for fractional evolution equations of parabolic type, J. Appl. Math. Stoch. Anal., 3(2004), 197-211.
    • (2004) J. Appl. Math. Stoch. Anal , vol.3 , pp. 197-211
    • El-Borai, M.M.1
  • 30
    • 80051576826 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional control systems in Banach spaces
    • J. Wang, Y. Zhou, Analysis of nonlinear fractional control systems in Banach spaces, Non- linear Anal.:TMA, 74(2011), 5929-5942.
    • (2011) Non- Linear Anal.:TMA , vol.74 , pp. 5929-5942
    • Wang, J.1    Zhou, Y.2
  • 31
    • 79960842094 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional delay evolution systems, Appl
    • J. Wang, Y. Zhou, Existence of mild solutions for fractional delay evolution systems, Appl. Math. Comput., 218(2011), 357-367.
    • (2011) Math. Comput , vol.218 , pp. 357-367
    • Wang, J.1    Zhou, Y.2
  • 32
    • 79961010111 scopus 로고    scopus 로고
    • Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls
    • J. Wang, Y. Zhou, W. Wei, H. Xu, Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls, Comput. Math. Appl., 62(2011), 1427-1441.
    • (2011) Comput. Math. Appl , vol.62 , pp. 1427-1441
    • Wang, J.1    Zhou, Y.2    Wei, W.3    Xu, H.4
  • 33
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • J. Wang, Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal.:RWA, 12(2011), 262-272.
    • (2011) Nonlinear Anal.:RWA , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 34
    • 79952206282 scopus 로고    scopus 로고
    • Study of an approximation process of time optimal control for fractional evolution systems in Banach spaces
    • 2011, Article ID 385324
    • J. Wang, Y. Zhou, Study of an approximation process of time optimal control for fractional evolution systems in Banach spaces, Adv. Difference Equ., 2011(2011), Article ID 385324, 16pp.
    • (2011) Adv. Difference Equ , pp. 16
    • Wang, J.1    Zhou, Y.2
  • 35
    • 79955979032 scopus 로고    scopus 로고
    • A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces
    • J. Wang, Y. Zhou, W. Wei, A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces, Commun. Nonlinear Sci. Numer. Simulat., 16(2011), 4049-4059.
    • (2011) Commun. Nonlinear Sci. Numer. Simulat , vol.16 , pp. 4049-4059
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 36
    • 77955515765 scopus 로고    scopus 로고
    • Nonlocal Cauchy problem for fractional evolution equations
    • Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal.:RWA, 11(2010), 4465-4475.
    • (2010) Nonlinear Anal.:RWA , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 37
    • 74149093181 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional neutral evolution equations
    • Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comp. Math. Appl., 59(2010), 1063-1077.
    • (2010) Comp. Math. Appl , vol.59 , pp. 1063-1077
    • Zhou, Y.1    Jiao, F.2
  • 38
    • 50349092768 scopus 로고    scopus 로고
    • Existence of the mild solution for fractional semilinear initial value problems
    • O. K. Jaradat, A. Al-Omari, S. Momani, Existence of the mild solution for fractional semilinear initial value problems, Nonlinear Anal.:TMA, 69(2008), 3153-3159.
    • (2008) Nonlinear Anal.:TMA , vol.69 , pp. 3153-3159
    • Jaradat, O.K.1    Al-Omari, A.2    Momani, S.3
  • 39
    • 78149482884 scopus 로고    scopus 로고
    • On the existence of mild solutions to some semilinear fractional integro-differential equations
    • T. Diagana, G. Mophou and G. N'gúeŕekata, On the existence of mild solutions to some semilinear fractional integro-differential equations, Electron. J. Qual. Theory Differ. Equ., No. 58(2010), 1-17.
    • (2010) Electron. J. Qual. Theory Differ. Equ , vol.58 , pp. 1-17
    • Diagana, T.1    Mophou, G.2    Ngúeŕekata, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.