Wellposedness and controllability results of stochastic integrodifferential equations with noninstantaneous impulses and Rosenblatt process
Tóm tắt
The purpose of this work is to investigate a novel class of noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct a new set of adequate assumptions for the existence and uniqueness of mild solutions using stochastic analysis, analytic semigroup theory, integral equation theory, and a fixed point methodology. Additionally, we study the asymptotic behavior of mild solutions and provide stochastic system controllability results. Finally, we include an example to illustrate the application of our main findings.
Tài liệu tham khảo
Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (2014)
Mao, X.: Stochastic Differential Equations and Applications. Horwood publishing series in mathematics & applications. Horwood Publishing Limited, Chichester (1997)
Øksendal, B.: Stochastic differential equations: An introduction with applications. Springer, Berlin (2003)
Boufoussi, B., Hajji, S.: Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space. Stat. Probab. Lett. 82(8), 1549–1558 (2012)
Chadha, A., Pandey, D.N.: Existence results for an impulsive neutral stochastic fractional integro-differential equation with infinite delay. Nonlinear Anal. 128, 149–175 (2015)
Dhanalakshmi, K., Balasubramaniam, P.: Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process. Stoch. Anal. Appl. 38(2), 352–372 (2020)
Tudor, C.A.: Analysis of the Rosenblatt process. ESAIM Probab. Stat. 12, 230–257 (2008)
Saravanakumar, S., Balasubramaniam, P.: On impulsive Hilfer fractional stochastic differential system driven by Rosenblatt process. Stoch. Anal. Appl. 37(6), 955–976 (2019)
Kasinathan, R., Kasinathan, R., Hamit, M.H., Diop, M.A.: Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process. Nonauton. Dyn. Syst. 7(1), 1–21 (2020)
Ramkumar, K., Ravikumar, K., Anguraj, A., Ahmed, H.M.: Well posedness results for higher-order neutral stochastic differential equations driven by Poisson jumps and Rosenblatt process. Filomat 35(2), 353–365 (2021)
Wang, J., Feckan, M., Debbouche, A.: Time optimal control of a system governed by non-instantaneous impulsive differential equations. J. Optim. Theory Appl. 182(2), 573–587 (2019)
Dhayal, R., Malik, M., Existence, A.S.: stability and controllability results of stochastic differential equations with non-instantaneous impulses. Int. J. Control 13, 1–2 (2021)
Malik, M., Dhayal, R., Abbas, S., Kumar, A.: Controllability of non-autonomous nonlinear differential system with non-instantaneous impulses. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 113(1), 103–118 (2019)
Agarwal, R., Hristova, S., O’Regan, D.: Non-instantaneous Impulses in Differential Equations. Springer, Berlin (2017)
Bai, L., Nieto, J.J., Uzal, J.M.: On a delayed epidemic model with non-instantaneous impulses. Commun. Pure Appl. Anal. 19(4), 1915–1930 (2020)
Bai, L., Nieto, J.J.: Variational approach to differential equations with not instantaneous impulses. Appl. Math. Lett. 73, 44–48 (2017)
Malik, M., Dhayal, R., Abbas, S.: Exact controllability of a retarded fractional differential equation with non-instantaneous impulses. Dyn. Contin. Discrete Impuls. Syst. 26, 53–69 (2019)
Singh, V.: Controllability of hilfer fractional differential systems with non-dense domain. Numer. Funct. Anal. Optim. 40(13), 1572–1592 (2019)
Singh, V., Pandey, D.N.: Controllability of multi-term time-fractional differential systems. J. Control Decis. 7(2), 109–125 (2020)
Chadha, A., Bora, S.N., Sakthivel, R.: Approximate controllability of impulsive stochastic fractional differential equations with nonlocal conditions. Dyn. Syst. Appl. 27(1), 1–29 (2018)
Anguraj, A., Ramkumar, K., Ravikumar, K.: Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with fractional Brownian motion and Poisson jumps. Discont. Nonlinearity Complex. 10(2), 227–235 (2021)
Anguraj, A., Ramkumar, K.: Approximate controllability of semilinear stochastic integrodifferential system with nonlocal conditions. Fractal Fract. 2(4), 29 (2018)
Anguraj, A., Ravikumar, K., Baleanu, D.: Approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps. Adv. Differ. Equ. 2020(1), 1 (2020)
Yan, Z., Jia, X.: Approximate controllability of impulsive fractional stochastic partial neutral integrodifferential inclusions with infinite delay. IMA J. Math. Control Inf. 34(3), 779–820 (2017)
Klamka, J.: Controllability of linear dynamical systems. Contrib. Theory Differ. Equ. 1, 189–213 (1963)
Naito, K.: Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25(3), 715–722 (1987)
Diop, A., Diop, M.A., Ezzinbi, K., Man, A.: Existence and controllability results for nonlocal stochastic integro-differential equations. Stochastics 93(6), 833–856 (2021)
Chalishajar, D., Ramkumar, K., Anguraj, A., Ravikumar, K., Diop, M.A.: Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator. J. Nonlinear Sci. Appl. 15(3), 172–185 (2022)
Sathiyaraj, T., Wang, J., Balasubramaniam, P.: Controllability and optimal control for a class of time-delayed fractional stochastic integro-differential systems. Appl. Math. Optim. 84(3), 2527–2554 (2021)
Sathiyaraj, T., Wang, J., O’Regan, D.: Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution. Proc. R. Soc. Edinb., Sect. A, Math. 151(1), 217–239 (2021)
Dhayal, R., Malik, M., Abbas, S., Debbouche, A.: Optimal controls for second-order stochastic differential equations driven by mixed-fractional Brownian motion with impulses. Math. Methods Appl. Sci. 43(7), 4107–4124 (2020)
Liu, S., Wang, J.: Optimal controls of systems governed by semilinear fractional differential equations with not instantaneous impulses. J. Optim. Theory Appl. 174(2), 455–473 (2017)
Dhayal, R., Malik, M., Abbas, S.: Approximate and trajectory controllability of fractional stochastic differential equation with non-instantaneous impulses and poisson jumps. Asian J. Control 23, 2669–2680 (2021)
Huan, D.D.: On the controllability of nonlocal second-order impulsive neutral stochastic integro-differential equations with infinite delay. Asian J. Control 17(4), 1233–1242 (2015)
Yan, Z., Jia, X.: Existence and controllability results for a new class of impulsive stochastic partial integro-differential inclusions with state-dependent delay. Asian J. Control 19(3), 874–899 (2017)
Hale, J.K., Kato, J.: Phase Space for Retarded Equations with Infinite Delay. Funkc. Ekvacioj 21, 11–41 (1978)
Marle, C.M.: Measures et Probabilities. Hermann, Paris (1974)
Grimmer, R.C.: Resolvent operator for integral equations in a Banach space. Am. Math. Soc. 13, 333–349 (1982)