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Approximate controllability of fractional order semilinear delay systems. (English) Zbl 1251.93039
Summary: In this paper, the approximate controllability for a class of semilinear delay control systems of fractional order is proved under the natural assumption that the linear system is approximately controllable. The existence and uniqueness of the mild solution is also proved under suitable assumptions. An example is given to illustrate our main results.

93B05 Controllability
93C05 Linear systems in control theory
93C25 Control/observation systems in abstract spaces
34A08 Fractional ordinary differential equations
Full Text: DOI
[1] Abd El-Ghaffar, A., Moubarak, M.R.A., Shamardan, A.B.: Controllability of fractional nonlinear control system. J. Fractional Calc. 17, 59–69 (2000) · Zbl 0964.93014
[2] Balachandran, K., Park, J.Y.: Controllability of fractional integrodifferential systems in Banach spaces. Nonlinear Anal. Hybrid Syst 3, 363–367 (2009) · Zbl 1175.93028
[3] Bragdi, M., Hazi, M.: Existence and controllability result for an evolution fractional integrodifferential systems. Int. J. Contemp. Math. Sci. 5(19), 901–910 (2010) · Zbl 1206.93015
[4] Tai, Z., Wang, X.: Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces. Appl. Math. Lett. 22, 1760–1765 (2009) · Zbl 1181.34078
[5] Triggiani, R.: A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J. Control Optim. 15, 407–411 (1977) · Zbl 0354.93014
[6] Dauer, J.P., Mahmudov, N.I.: Approximate controllability of semilinear functional equations in Hilbert spaces. J. Math. Anal. Appl. 273, 310–327 (2002) · Zbl 1017.93019
[7] Sukavanam, N., Tomar, N.K.: Approximate controllability of semilinear delay control systems. Nonlinear Funct. Anal. Appl. 12(1), 53–59 (2007) · Zbl 1141.93016
[8] Jeong, J.M., Kim, J.R., Roh, H.H.: Controllability for semilinear retarded control systems in Hilbert spaces. J. Dyn. Control Syst. 13(4), 577–591 (2007) · Zbl 1139.35015
[9] Jeong, J.M., Kim, H.G.: Controllability for semilinear functional integrodifferential equations. Bull. Korean Math. Soc. 46(3), 463–475 (2009) · Zbl 1170.35332
[10] Bian, W.: Approximate controllability for semilinear systems. Acta Math. Hung. 81(1–2), 41–57 (1998) · Zbl 1108.93302
[11] Chukwu, E.N., Lenhart, S.M.: Controllability question for nonlinear systems in abstract space. J. Optim. Theory Appl. 68(3), 437–462 (1991) · Zbl 0697.49040
[12] Sukavanam, N.: Divya: Approximate controllability of abstract semilinear deterministic control system. Bull. Calcutta Math. Soc. 96(3), 195–202 (2004) · Zbl 1113.93305
[13] Wang, L.W.: Approximate controllability for integrodifferential equations with multiple delays. J. Optim. Theory Appl. 143, 185–206 (2009) · Zbl 1176.93018
[14] Naito, K., Park, J.Y.: Approximate controllability for trajectories of a delay Volterra control system. J. Optim. Theory Appl. 61(2), 271–279 (1989) · Zbl 0644.93009
[15] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) · Zbl 1092.45003
[16] Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993) · Zbl 0789.26002
[17] Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999) · Zbl 0924.34008
[18] Hu, L., Ren, Y., Sakthivel, R.: Existence and uniqueness of mild solution for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays. Semigroup Forum 79, 507–514 (2009) · Zbl 1184.45006
[19] Tomara, N.K., Sukavanama, N.: Exact controllability of a semilinear thermoelastic system with control solely in thermal equation. Numer. Funct. Anal. Optim. 29(9–10), 1171–1179 (2008) · Zbl 1151.93007
[20] Naito, K.: Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25(3), 715–722 (1987) · Zbl 0617.93004
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