Boundary Controllability of Fractional Order Nonlocal Semi-linear Neutral Evolution Systems with Impulsive Condition
DOI:
https://doi.org/10.5890/DNC.2019.12.006Abstract
Sufficient conditions of boundary controllability of fractional nonlocal semi-linear neutral evolution equations with impulsive conditions are demonstrated. To get the result, we employ fixed point theorem and strongly continuous semi-group theory. An application is discussed to explain the theory.References
[1] Balachandran, K. and Anandhi, E.R. (2003), Neutral functional integrodifferential control systems in Banach spaces, Ky-bernetika, 39, 359-367.
[2] Fu, X.L. (2003), Controllability of neutral functional differential systems in abstract space, Appl. Math Comput., 141, 281-296.
[3] Balakrishnan, A.V. (1976), Applied Functional Analysis, Springer-Verlag, New York.
[4] Washburn, D. (1979), A bound on the boundary input map for parabolic equations with application to time optimal control, SIAM J Control Optim., 17, 652-671.
[5] Fattorini, H.O. (1968), Boundary control systems, SIAM J Control Optim., 6, 349-384.
[6] Lasiecka, T. (1978), Boundary Control of Parabolic Systems; Regularity of Solutions, Appl. Math Optim., 4, 301-327.
[7] Balachandran, K. and Anandhi, E.R. (2004), Boundary controllability of neutral integrodifferential systems in Banach spaces, Nihonkai Math. J., 15, 1-13.
[8] Balachandran, K. and Leelamani, A. (2006), A note on boundary controllability of neutral integrodifferential systems in Banach spaces, Nihonkai Math. J., 17, 89-101.
[9] Park, J.Y. and Jeong, J.U. (2011), Boundary controllability of semilinear neutral evolution systems, Bull Korean Math Soc., 48(4), 705-712.
[10] Oustaloup, A. (1995), La Derivation Non Entiere: Theorie, Syntheseet Applications, Hermes, Paris.
[11] Lakshmikantham, V., Bainov, D.D., and Simeonov, P.S. (1989), Theory of impulsive differential equations, Series in Modern Applied Mathematics,World Scientific Publishing, New Jersey.
[12] Perestyuk, N.A., Plotnikov, V.A., Samoilenko, A.M., and Skripnik, N.V. (2011), Differential equation with impulse effects: Multivalued Right-hand Side with discontinuities, De Gruyter Studies in Mathematics 40, Germany.
[13] Ahmed, H.M. (2010), Boundary controllability of nonlinear fractional integrodifferential systems, Adv Differ Equat., 2010, Article ID 279493, 9 pages.
[14] Ahmed, H.M. (2016), Boundary controllability of impulsive nonlinear fractional delay integrodifferential system, Cogent Engineering, 3(1), 1-8.
[15] Kumar, K. and Kumar, R. (2017), Boundary controllability of delay differential systems of fractional order with nonlocal condition, Journal of Applied Nonlinear Dynamics, 6(4), 465-472.
[16] Zhou, Y. and Jiao, F. (2010), Existence of mild solutions for fractional neutral evolution equations, Computers and Mathematics with Applications, 59, 1063-1077.
[17] Pazy, A. (1983), Semi-groups of linear operators and applications to partial differential equations, Springer, New York.
[18] Podlubny, I. (1999), Fractional Differential Equations, Academic Press, San Diego.
[19] Samko, S., Kilbas, A., andMarichev, O.L. (1993), Fractional integrals and derivatives, Gordon and Breach, New York.
[20] Miller, K.S. and Ross, B. (1993), An introduction to the fractional calculus and fractional differential equations,Wiley, New York.
[21] El-Borai,M.M. (2002), Some probability densities and fundamental solutions of fractional evolution equations, Chaos, Soli-tons and Fracts, 14(3), 433-440.
[22] El-Borai, M.M. (2006), On some stochastic fractional integrodifferential equations, Advances in Dynamical Systems and Applications, 1(1), 49-57.
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