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On controllability of fractional impulsive neutral infinite delay evolution integrodifferential systems in Banach spaces. (English) Zbl 1236.93024
Summary: In this work, controllability of fractional impulsive neutral evolution integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, resolvent operators and Krasnosel’skii’s fixed point theorem.

93C30Control systems governed by other functional relations
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34K37Functional-differential equations with fractional derivatives
Full Text: DOI
[1] Sakthivel, R.: Existence and controllability result for semilinear evolution integrodifferential systems, Math. comput. Modelling 41, 1005-1011 (2005) · Zbl 1129.93005 · doi:10.1016/j.mcm.2004.03.007
[2] Sakthivel, R.: Controllability result for nonlinear evolution integrodifferential systems, Appl. math. Lett. 17, 1015-1023 (2004) · Zbl 1072.93005 · doi:10.1016/j.aml.2004.07.003
[3] Sakthivel, R.: Controllability of nonlinear neutral evolution integrodifferential systems, J. math. Anal. appl. 275, 402-417 (2002) · Zbl 1010.93055 · doi:10.1016/S0022-247X(02)00375-X
[4] Balachandran, K.; Leelamani, A.; Kim, J. -H.: Controllability of neutral functional evolution integrodifferential systems with infinite delay, IMA J. Math. control inf. 25, 157-171 (2008) · Zbl 1146.93006 · doi:10.1093/imamci/dnm013
[5] Park, J. Y.: Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces, Nonlinear anal.: hybrid syst. (2008)
[6] Chang, Y. K.: Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos solitons fractals 33, 1601-1609 (2007) · Zbl 1136.93006 · doi:10.1016/j.chaos.2006.03.006
[7] Balachandran, K.; Park, J. Y.: Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear anal. Hybrid syst. (2009) · Zbl 1175.93028
[8] Bonilla, B.; Rivero, M.; Rodriguez-Germa, L.; Trujillo, J. J.: Fractional differential equations as alternative models to nonlinear differential equations, Appl. math. Comput. 187, 79-88 (2007) · Zbl 1120.34323 · doi:10.1016/j.amc.2006.08.105
[9] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993) · Zbl 0789.26002
[10] Smart, D. R.: Fixed point theorems, (1980) · Zbl 0427.47036