Open Access
Subscription Access
Open Access
Subscription Access
Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces
Subscribe/Renew Journal
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.
Subscription
Login to verify subscription
User
Font Size
Information
- 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.
Abstract Views: 424
PDF Views: 0