Balachandran, K.; Park, J. Y. Controllability of fractional integrodifferential systems in Banach spaces. (English) Zbl 1175.93028 Nonlinear Anal., Hybrid Syst. 3, No. 4, 363-367 (2009). Summary: We study the controllability of fractional integrodifferential systems in Banach spaces. The results are obtained by using fractional calculus, semigroup theory and a fixed point theorem. Cited in 46 Documents MSC: 93B05 Controllability 93C25 Control/observation systems in abstract spaces 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics Keywords:controllability; integrodifferential system; semigroup theory; fractional calculus; fixed point theorem PDF BibTeX XML Cite \textit{K. Balachandran} and \textit{J. Y. Park}, Nonlinear Anal., Hybrid Syst. 3, No. 4, 363--367 (2009; Zbl 1175.93028) Full Text: DOI References: [1] 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 [2] Delbosco, D.; Rodino, L., Existence and uniqueness for a fractional differential equation, Journal of Mathematical Analysis and Applications, 204, 609-625 (1996) · Zbl 0881.34005 [3] Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear Analysis, 69, 3337-3343 (2008) · Zbl 1162.34344 [4] Lakshmikantham, V.; Vatsala, A. S., Basic theory of fractional differential equations, Nonlinear Analysis, 69, 2677-2682 (2008) · Zbl 1161.34001 [5] Lakshmikantham, V.; Vatsala, A. S., General uniqueness and monotone iterative technique for fractional differential equations, Applied Mathematics Letters, 21, 828-834 (2008) · Zbl 1161.34031 [6] Lakshmikantham, V.; Vasundhara Devi, J., Theory of fractional differential equations in Banach spaces, European Journal of Pure and Applied Mathematics, 1, 38-45 (2008) · Zbl 1146.34042 [7] Bonnet, C.; Partington, J. R., Coprime factorizations and stability of fractional differential systems, Systems and Control Letters, 41, 167-174 (2000) · Zbl 0985.93048 [8] Nec, Y.; Nepomnyashchy, A. A., Linear stability of fractional reaction-diffusion systems, Mathematical Modelling of Natural Phenomena, 2, 77-105 (2007) · Zbl 1337.35076 [9] El-Sayeed, M. A.A., Fractional order diffusion wave equation, International Journal of Theoretical Physics, 35, 311-322 (1966) · Zbl 0846.35001 [10] Klamka, J., Controllability of Dynamical Systems (1993), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0818.93002 [11] Curtain, R. F.; Pritchard, A. J., Infinite Dimensional Linear Systems Theory (1978), Springer-Verlag: Springer-Verlag New York · Zbl 0389.93001 [12] Balachandran, K.; Dauer, J. P., Controllability of nonlinear systems via fixed point theorem, Journal of Optimization Theory and Applications, 53, 345-352 (1987) · Zbl 0596.93010 [13] Balachandran, K.; Dauer, J. P., Controllability of nonlinear systems in Banach spaces; A survey, Journal of Optimization Theory and Applications, 115, 7-28 (2002) · Zbl 1023.93010 [14] Abd El-Ghaffar, A.; Moubarak, M. R.A.; Shamardan, A. B., Controllability of fractional nonlinear control system, Journal of Fractional Calculus, 17, 59-69 (2000) · Zbl 0964.93014 [15] Chen, Y. Q.; Ahu, H. S.; Xue, D., Robust controllability of interval fractional order linear time invariant systems, Signal Processing, 86, 2794-2802 (2006) · Zbl 1172.94386 [16] Shamardan, A. B.; Moubarak, M. R.A., Controllability and observability for fractional control systems, Journal of Fractional Calculus, 15, 25-34 (1999) · Zbl 0964.93013 [17] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Elsevier: Elsevier Amsterdam · Zbl 1092.45003 [18] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley: Wiley New York · Zbl 0789.26002 [19] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press New York · Zbl 0918.34010 [20] Jaradat, O. K.; Al-Omari, A.; Momani, S., Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69, 3153-3159 (2008) · Zbl 1160.34300 [21] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0516.47023 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.