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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.

34K35Functional-differential equations connected with control problems
34K45Functional-differential equations with impulses
34K30Functional-differential equations in abstract spaces
34K40Neutral functional-differential equations
47N20Applications of operator theory to differential and integral equations
93C23Systems governed by functional-differential equations
Full Text: DOI
[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 · doi:10.1016/j.camwa.2005.03.001
[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 · doi:10.1016/j.chaos.2005.08.041
[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 · doi:10.1093/imamci/dnm013
[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 · doi:10.1016/j.chaos.2006.03.006
[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) · Zbl 0789.26002
[10] Smart, D. R.: Fixed point theorems, (1980) · Zbl 0427.47036