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Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces. (English) Zbl 1181.34078
Summary: The controllability of fractional impulsive neutral functional integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, a semigroup of operators and Krasnoselskii’s fixed point theorem.

MSC:
34K35 Control problems for functional-differential equations
34K45 Functional-differential equations with impulses
34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
93B05 Controllability
47N20 Applications of operator theory to differential and integral equations
93C23 Control/observation systems governed by functional-differential equations
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[1] Balachandran, K.; Park, D.G., Controllability of second-order integrodifferential evolution systems in Banach spaces, Computers and mathematics with applications, 49, 1623-1642, (2005) · Zbl 1127.93013
[2] Li, M.; Wang, M.; Zhang, F., Controllability of impulsive functional differential systems in Banach spaces, Chaos, solitons and fractals, 29, 175-181, (2006) · Zbl 1110.34057
[3] Balachandran, K.; Leelamani, A.; Kim, J.-H., Controllability of neutral functional evolution integrodifferential systems with infinite delay, IMA journal of mathematical control and information, 25, 157-171, (2008) · Zbl 1146.93006
[4] Park, J.Y., Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces, Nonlinear analysis: hybrid systems, (2008)
[5] Balachandran, K.; Park, J.Y., Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear analysis: hybrid systems, (2009) · Zbl 1175.93028
[6] Chang, Y.K., Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos, solitons and fractals, 33, 1601-1609, (2007) · Zbl 1136.93006
[7] Bonilla, B.; Rivero, M.; Rodriguez-Germa, L.; Trujillo, J.J., Fractional differential equations as alternative models to nonlinear differential equations, Applied mathematics and computation, 187, 79-88, (2007) · Zbl 1120.34323
[8] El-Sayeed, M.A.A., Fractional order diffusion wave equation, International journal of theoretical physics, 35, 311-322, (1966)
[9] Miller, K.S.; Ross, B., An introduction to the fractional calculus and fractional differential equations, (1993), Wiley New York · Zbl 0789.26002
[10] Smart, D.R., Fixed point theorems, (1980), Cambridge University Press Cambridge · Zbl 0427.47036
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