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.


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
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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.