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Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces
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In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.
Keywords
Approximate Controllability, Fixed Point Theorems, Stochastic Differential Equation, Mild Solution.
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- Agarwal, S., & Bahuguna, D., Existence of solutions to Sobolev-type partial neutral differential equations, Journal of Applied Mathematics and Stochastic Analysis, 1-10. (2006), Article ID 16308.
- Arnold, L., Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, (1974).
- Balasubramaniam, P., & Tamilalagan, P., Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function, Applied Mathematics and Computation, 256 (2015), 232-246.
- Benchohra, M., Henderson, J. Ntouyas, S.K., & Ouahab, A., Existence results for fractional order functional differential equations with infinite delay, Journal of Mathematical Analysis and Applications, 338 (2008), 1340-1350.
- Brill, H., A semilinear Sobolev evolution equation in Banach space, Journal of Differential Equations, 24(1977), 412-425.
- Chalishajar, D.N., Controllability of second order impulsive neutral functional differential inclusions with infinite delay, Journal of Optimization Theory and Applications, 154 (2)(2012), 672-684.
- Chang, Y.K., & Li, W.T., Controllability of Sobolev type semilinear functional differential and integrodifferential inclusions with an unbounded delay, Georgian Mathematical Journal, 13 (1)(2006), 11-24.
- Chang, Y.K., Controllability of impulsive functional differential systems with infinite delay in Banach space, Chaos Solitons Fractals, 33(2007), 1601-1609.
- Da Prato, G., & Zabczyk, J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, (1992).
- Dauer, J.P., & Mahmudov, N.I., Controllability of stochastic semilinear functional differential equations in Hilbert spaces, Journal of Mathematical Analysis and Applications, 290(2004), 373-394.
- Kucche, K.D., & Dhakne, M.B., Sobolev-type Volterra-Fredholm functional integrodifferential equations in Banach spaces, Boletim da Sociedade Paranaense de Matematica, 32 (1)(2014) , 237-253.
- Lunardi, A., On the linear heat equation with fading memory, SIAM Journal on Mathematical Analysis, 21 (5)(1990), 1213-1224.
- Mahmudov, N.I., Controllability of linear stochastic systems in Hilbert spaces, Journal of Mathematical Analysis and Applications, 259(2001), 64-82.
- Mahmudov, N.I., Approximate controllability of fractional Sobolev-type evolution equations in Banach spaces, Abstract and Applied Analysis, 1-9(2013), Article ID 502839.
- Mahmudov, N.I., Existence and approximate controllability of Sobolev type fractional stochastic evolution equations, Bulletin of the Polish Academy of Sciences Technical Sciences, 62 (2)(2014), 205-215.
- Mahmudov, N.I, & Denker, A., Controllability of linear stochastic systems, International Journal of Control, 73(2000), 144-151.
- Mahmudov, N.I., Vijayakumar, V., & Murugesu, R. Approximate controllability of second-order evolution differential inclusions in Hilbert spaces, Mediterranean Journal of Mathematics, 13 (5)(2016), 3433-3454.
- Oksendal, B., 2000, Stochastic Differential Equations, An Introduction with Applications, Springer-Verlag,(2000).
- Park, J.Y, Balasubramaniam, P, & Kumaresan, N., Controllability for neutral stochastic functional integrodifferential infinite delay systems in abstract space, Numerical Functional Analysis and Optimization, 28(2007), 1369-1386 .
- Ren, Y, & Sun, D.D., Second-order neutral stochastic evolution equations with infinite delay under Caratheodory conditions, Journal of Optimization Theory and Applications, 147(2010), 569-582.
- Revathi, P., Sakthivel, R., & Ren, Y., Stochastic functional differential equations of Sobolev-type with infinite delay, Statistics & Probability Letters, 109(2016), 68-77.
- Sakthivel, R, Mahmudov, N.I, Lee, S.G., Controllability of non-linear impulsive stochastic systems, International Journal of Control, 82(2009), 801-807.
- Shen, L.J,& Sun, J.T., 2012, Approximate controllability of stochastic impulsive functional systems with infinite delay, Automatica 48(2012), 2705-2709.
- Vijayakumar, V., Ravichandran, C., Murugesu, R., & Trujillo, J.J., Controllability results for a class of fractional semilinear integro-differential inclusions via resolvent operators, Applied Mathematics and Computation, 247(2014), 152-161.
- Vijayakumar, V., Approximate controllability results for abstract neutral integrodifferential inclusions with infinite delay in Hilbert spaces, IMA Journal of Mathematical Control and Information,1-18(2016), doi: 10.1093/imamci/dnw049.
- Vijayakumar, V., Approximate controllability results for analytic resolvent integrodifferential inclusions in Hilbert spaces, International Journal of Control, 1-11(2017), DOI:10.1080/00207179.2016.1276633.
- Wang, J., Feckan, M., & Zhou, Y., Controllability of Sobolev type fractional evolution systems, Dynamics of Partial Differential Equations, 11 (1)(2014), 71-87.
- Wu, J., & Xia, H., Rotating waves in neutral partial functional-differential equations, Journal of Dynamics and Differential Equations, 11 (2)(1999), 209-238.
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