Existence results for some stochastic functional integrodifferential systems driven by Rosenblatt process

References

[1] H. M. Ahmed, Approximate controllability of impulsive neutral stochastic differential equations with fractional Brownian motion in a Hilbert space, Adv. Difference Equ. 2014 (2014), 1–11. 10.1186/1687-1847-2014-113Search in Google Scholar

[2] A. Anguraj and K. Ravikumar, Existence and stability results for impulsive stochastic functional integro-differential equation with Poisson jumps, J. Appl. Nonlinear Dyn. 8 (2019), no. 3, 407–417. 10.5890/JAND.2019.09.005Search in Google Scholar

[3] D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge Stud. Adv. Math. 116, Cambridge University, Cambridge, 2009. 10.1017/CBO9780511809781Search in Google Scholar

[4] J.-M. Bardet and C. A. Tudor, A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter, Stochastic Process. Appl. 120 (2010), no. 12, 2331–2362. 10.1016/j.spa.2010.08.003Search in Google Scholar

[5] T. Blouhi, T. Caraballo and A. Ouahab, Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion, Stoch. Anal. Appl. 34 (2016), no. 5, 792–834. 10.1080/07362994.2016.1180994Search in Google Scholar

[6] T. Caraballo, M. J. Garrido-Atienza and T. Taniguchi, The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion, Nonlinear Anal. 74 (2011), no. 11, 3671–3684. 10.1016/j.na.2011.02.047Search in Google Scholar

[7] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University, Cambridge, 1992. 10.1017/CBO9780511666223Search in Google Scholar

[8] B. de Andrade and J. P. C. dos Santos, Existence of solutions for a fractional neutral integro-differential equation with unbounded delay, Electron. J. Differential Equations 2012 (2012), 1–13. Search in Google Scholar

[9] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985. 10.1007/978-3-662-00547-7Search in Google Scholar

[10] S. Deng, X.-B. Shu and J. Mao, Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point, J. Math. Anal. Appl. 467 (2018), no. 1, 398–420. 10.1016/j.jmaa.2018.07.002Search in Google Scholar

[11] W. Desch, R. Grimmer and W. Schappacher, Some considerations for linear integro-differential equations, J. Math. Anal. Appl. 104 (1984), no. 1, 219–234. 10.1016/0022-247X(84)90044-1Search in Google Scholar

[12] A. Diop, M. A. Diop, O. Diallo and M. B. Traoré, Local attractivity for integro-differential equations with noncompact semigroups, Nonauton. Dyn. Syst. 7 (2020), no. 1, 102–117. 10.1515/msds-2020-0113Search in Google Scholar

[13] K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math. 194, Springer, New York, 2000. Search in Google Scholar

[14] K. Ezzinbi, G. Degla and P. Ndambomve, Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces, Discuss. Math. Differ. Incl. Control Optim. 35 (2015), no. 1, 25–46. 10.7151/dmdico.1167Search in Google Scholar

[15] K. Ezzinbi, H. Toure and I. Zabsonre, Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces, Nonlinear Anal. 70 (2009), no. 9, 3378–3389. 10.1016/j.na.2008.05.006Search in Google Scholar

[16] D. Gao and J. Li, Existence results for impulsive delayed neutral stochastic functional differential equations with noncompact semigroup, Stochastics 93 (2021), no. 8, 1209–1226. 10.1080/17442508.2021.1873340Search in Google Scholar

[17] R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 (1982), no. 1, 333–349. 10.1090/S0002-9947-1982-0664046-4Search in Google Scholar

[18] R. C. Grimmer and F. Kappel, Series expansions for resolvents of Volterra integro-differential equations in Banach space, SIAM J. Math. Anal. 15 (1984), no. 3, 595–604. 10.1137/0515045Search in Google Scholar

[19] R. C. Grimmer and A. J. Pritchard, Analytic resolvent operators for integral equations in Banach space, J. Differential Equations 50 (1983), no. 2, 234–259. 10.1016/0022-0396(83)90076-1Search in Google Scholar

[20] G. Gripenberg, S.-O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia Math. Appl. 34, Cambridge University, Cambridge, 1990. 10.1017/CBO9780511662805Search in Google Scholar

[21] H. R. Henríquez and J. P. C. dos Santos, Differentiability of solutions of abstract neutral integro-differential equations, J. Integral Equations Appl. 25 (2013), no. 1, 47–77. 10.1216/JIE-2013-25-1-47Search in Google Scholar

[22] E. Hernández M, H. R. Henríquez and J. P. C. dos Santos, Existence results for abstract partial neutral integro-differential equation with unbounded delay, Electron. J. Qual. Theory Differ. Equ. 29 (2009), 1–23. 10.14232/ejqtde.2009.1.29Search in Google Scholar

[23] S. Ji and M. Wang, Solutions to impulsive integrodifferential evolution equations under a noncompact evolution system, Adv. Difference Equ. 2015 (2015), 1–13. 10.1186/s13662-015-0638-9Search in Google Scholar

[24] Kamaljeet and D. Bahuguna, Approximate controllability of nonlocal neutral fractional integro-differential equations with finite delay, J. Dyn. Control Syst. 22 (2016), no. 3, 485–504. 10.1007/s10883-015-9297-0Search in Google Scholar

[25] V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Res. Notes in Math. Ser. 301, John Wiley & Sons, New York, 1994. Search in Google Scholar

[26] I. Kruk, F. Russo and C. A. Tudor, Wiener integrals, Malliavin calculus and covariance measure structure, J. Funct. Anal. 249 (2007), no. 1, 92–142. 10.1016/j.jfa.2007.03.031Search in Google Scholar

[27] E. H. Lakhel, Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion, Stoch. Anal. Appl. 34 (2016), no. 3, 427–440. 10.1080/07362994.2016.1149718Search in Google Scholar

[28] J. Liang, J. H. Liu and T.-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Modelling 49 (2009), no. 3–4, 798–804. 10.1016/j.mcm.2008.05.046Search in Google Scholar

[29] M. Maejima and C. A. Tudor, Wiener integrals with respect to the Hermite process and a non-central limit theorem, Stoch. Anal. Appl. 25 (2007), no. 5, 1043–1056. 10.1080/07362990701540519Search in Google Scholar

[30] M. Maejima and C. A. Tudor, On the distribution of the Rosenblatt process, Statist. Probab. Lett. 83 (2013), no. 6, 1490–1495. 10.1016/j.spl.2013.02.019Search in Google Scholar

[31] X. Mao, Stochastic Differential Equations and Applications, 2nd ed., Horwood, Chichester, 2007. 10.1533/9780857099402Search in Google Scholar

[32] J. Prüss, Evolutionary Integral Equations and Applications, Monogr. Math. 87, Birkhäuser, Basel, 1993. 10.1007/978-3-0348-8570-6Search in Google Scholar

[33] R. Ravi Kumar, Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), no. 1, 352–362. 10.1016/j.amc.2008.06.050Search in Google Scholar

[34] G. Shen and Y. Ren, Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space, J. Korean Statist. Soc. 44 (2015), no. 1, 123–133. 10.1016/j.jkss.2014.06.002Search in Google Scholar

[35] G. Shen, R. Sakthivel, Y. Ren and M. Li, Controllability and stability of fractional stochastic functional systems driven by Rosenblatt process, Collect. Math. 71 (2020), no. 1, 63–82. 10.1007/s13348-019-00248-3Search in Google Scholar

[36] C. A. Tudor, Analysis of the Rosenblatt process, ESAIM Probab. Stat. 12 (2008), 230–257. 10.1051/ps:2007037Search in Google Scholar

[37] X. Zhang, P. Chen, A. Abdelmonem and Y. Li, Fractional stochastic evolution equations with nonlocal initial conditions and noncompact semigroups, Stochastics 90 (2018), no. 7, 1005–1022. 10.1080/17442508.2018.1466885Search in Google Scholar

[38] G.-a. Zou, G. Lv and J.-L. Wu, Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises, J. Math. Anal. Appl. 461 (2018), no. 1, 595–609. 10.1016/j.jmaa.2018.01.027Search in Google Scholar