Acknowledgement
The authors would like to thank the referees and the editor for their careful comments and valuable suggestions to improve this manuscript.
References
- A. Anguraj, M. Mallika Arjunan, E. Hernandez, Existence results for an impulsive partial neutral functional differential equations with state-dependent delay, Appl. Anal. 86 (2007), 861-872. https://doi.org/10.1080/00036810701354995
- A. Anguraj, K. Ravikumar, Existence and stability results for impulsive stochastic functional integrodifferential equations with Poisson jumps, Journal of Applied Nonlinear Dynamics 8 (2019), 407-417. https://doi.org/10.5890/jand.2019.09.005
- A. Anguraj, K. Ramkumar, K. Ravikumar, Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays, Computational Methods for Differential Equations 10 (2022), 191-199.
- A. Anguraj, A. Vinodkumar, Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays, Electronic Journal of Qualitive Theory of Differential Equations 67 (2009), 1-13.
- A. Anguraj, A. Vinodkumar, Existence, uniqueness and stability results of random impulsive semilinear differential systems, Nonlinear Analysis: Hybrid Systems 3 (2010), 475-483. https://doi.org/10.1016/j.nahs.2009.03.006
- G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
- V. Gupta, F. Jarad, N. Valliammal, C. Ravichandran, K.S. Nisar, Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system, Numerical Methods for Partial Differential Equations 38 (2022), 359-371.
- E. Hernandez, M. Rabello, H.R. Henriquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Apll. 331 (2007), 1135-1158. https://doi.org/10.1016/j.jmaa.2006.09.043
- A. Kumar, H.V.S. Chauhan, C. Ravichandran, K.S. Nisar, D. Baleanu, Existence of solutions of non-autonomous fractional differential equations with integral impulse condition, Advances in Difference Equations 2020 (2020), 1-14. https://doi.org/10.1186/s13662-019-2438-0
- V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- S. Li, L. Shu, X.B. Shu, F. Xu, Existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delays, Stochastic 91 (2019), 1-16. https://doi.org/10.1080/17442508.2018.1499104
- N. Ngoc, Ulam-Hyers-Rassias stability of a nonlinear stochastic integral equation of Volterra type, Differ. Equ. Appl. 9 (2017), 183-193.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
- C. Ravichandrana, K. Logeswari, S.K. Panda, K.S. Nisar, On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions, Chaos, Solitons and Fractals 139 (2020), 110012.
- A.E. Rodkin, On existence and uniqueness of solutions of stochastic differential equations with heredity, Stochastic 12 (1984), 187-200. https://doi.org/10.1080/17442508408833300
- T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differential Equations 96 (1992), 152-169. https://doi.org/10.1016/0022-0396(92)90148-G
- T. Wang, S. Wu, Random impulsive model for stock prices and its application for insurers, Master thesis (in Chinese), Shanghai, East China Normal University, 2008.
- S.J. Wu, X.L. Guo, S.Q. Lin, Existence and uniqueness of solutions to random impulsive differential systems, Acta Math. Appl. Sin. 22 (2006), 595-600. https://doi.org/10.1007/s10114-005-0689-z
- S.J. Wu, X.Z. Meng, Boundedness of nonlinear differential systems with impulsive effect on random moments, Acta Math. Appl. Sin. 20 (2004), 147-154.
- S. Wu, B. Zhou, Existence and uniqueness of stochastic differential equations with random impulses and markovian switching under Non-Lipschitz conditions, J. Acta Math. Sin. 27 (2011), 519-536. https://doi.org/10.1007/s10114-011-9753-z
- X. Zhao, Mean square Hyers-Ulam stability of stochastic differential equations driven by Brownian motion, Adv. Difference. Equ. 2016 (2016), 1-12.