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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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References:

[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) · Zbl 0846.35001
[9] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley: Wiley New York · Zbl 0789.26002
[10] Smart, D. R., Fixed Point Theorems (1980), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0427.47036
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