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Exponential stability for higher-order impulsive fractional neutral stochastic integro-delay . . .

[19] Debbouche, A., & Nieto, J.J. (2015). Relax- Advances in Difference Equations, 112, 1-13. ht
ation in controlled systems described by fractional tps://doi.org/10.1186/1687-1847-2014-112
integro-differential equations with nonlocal con- [32] Arthi, G., Park, J.H., & Yung, H.Y. (2015). Expo-
trol conditions. Electronic Journal of Differential nential stability for second-order neutral stochas-
Equations,(89), 1-18. tic differential equations with impulses. Interna-
[20] Huan, D.D., & Gao, H. (2015). Controllability of tional Journal of Control, 88, 1300-1309. https:
nonlocal second-order impulsive neutral stochas- //doi.org/10.1080/00207179.2015.1006683
tic functional integro-differential equations with [33] Chen, H. (2010). Impulsive-integral inequality
delay and Poisson jumps. Cogent Engineering, 2, and exponential stability for stochastic partial
1-16. https://doi.org/10.1080/23311916.201 differential equations with delays. Statistics and
5.1065585 Probability Letters, 80, 50-56. https://doi.org/
[21] Muthukumar, P., & Rajivganthi, C. (2013). Ap- 10.1016/j.spl.2009.09.011
proximate controllability of fractional order neu- [34] Dhanalakshmi, K., & Balasubramaniam, P.
tral stochastic integro-differential systems with (2023). Ulam-Hyers stability for second-order
nonlocal conditions on infinite delay. Taiwanese non-instantaneous impulsive fractional neutral
Journal of Mathematics, 17, 1693-1713. https: stochastic differential equations. Journal of Math-
//doi.org/10.11650/tjm.17.2013.2743 ematical Physics, 64 (4), 042702.
[22] Revathi, P., Sakthivel, R., Song, D-Y., Ren, Y., [35] Dhanalakshmi, K., & Balasubramaniam, P.
& Zhang, P. (2017). Existence and stability re- (2023). Well posedness of second-order non-
sults for second-order stochastic equations driven instantaneous impulsive fractional neutral sto-
by fBm. Transport Theory and Statistical Physics, chastic differential equations. Bulletin des Sci-
42, 299-317. https://doi.org/10.1080/004114 ences Math´ematiques, 189, 103350.
50.2014.910813 [36] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J.
[23] Li, Q., Zhou, Y., & Zhao, X. (2014). Fractional (2006). Theory and applications of fractional dif-
order stochastic differential equation with appli- ferential equations. North-Holland Mathematics
cation in European option pricing. Discrete Dy- Studies. Elsevier, Amsterdam.
namics in Nature and Society, 7, 1-12. https: [37] Lakshmikantham, V., Leela, S., & Vasundhara
//doi.org/10.1155/2014/621895 Devi, J. (2009). Theory of fractional dynamic
[24] Hale, J.K., Sjoerd, M., & Verduyn, L. (1993). systems. Cambridge Scientific Publishers, United
Introduction to functional differential equations. Kingdom.
Springer-Verlag, New York. [38] Miller, K.S., & Ross, B. (1993). An Introduction
[25] Chadha, A. (2018). Exponential stability for neu- to the fractional calculus and differential equation.
tral stochastic partial integro-differential equa- John Willey, New York.
tions of second order with Poisson jumps. Filo- [39] Pazy, A. (1983). Semigroups of linear operator
mat, 32, 5173-5190. https://doi.org/10.2298/ and applications to partial differential equations.
FIL1815173C Springer, Berlin.
[26] Jiang, F., Yang, H., & Shen, Y. (2020). A note [40] Travis, C.C., & Webb, G.F. (1978). Cosine fami-
on exponential stability for second-order neutral lies and abstract nonlinear second order differen-
stochastic partial differential equations with infi- tial equation. Acta Mathematica. Academiae Sci-
nite delays in the presence of impulses. Applied entiarum Hungarica, 32, 76-96. https://doi.or
Mathematics and Computation, 125-133. g/10.1007/BF01902205
[27] Dhayal, R., Malik, M., Abbas, S., & Debbouche, [41] Travis, C.C., & Webb, G.F. (1977). Compact-
A. (2020). Optimal controls for second-order sto- ness, regularity, and uniform continuity proper-
chastic differential equations driven by mixed- ties of strongly continuous cosine families. Hous-
fractional Brownian motion with impulses. Math- ton Journal of Mathematics, 3, 555-567.
ematical Methods in the Applied Sciences, 43(7), [42] Travis, C.C., & Webb, G.F. (1987). Second or-
4107-4124. https://doi.org/10.1002/mma.61 der differential equations in Banach spaces. In
77 proceedings international symposium on nonlinear
[28] Lakshmikantham,V., Bainov, D.D., & Simeonov, equation in abstract spaces. New York: Academic
P.S.(1989). Theory of impulsive differential equa- Press, 331-361.
tions. World Scientific, Singapore. https://doi. [43] Granas, A., & Dugundji, J. (2003). Fixed point
org/10.1142/0906 theory. Springer-Verlag, New York. https://do
[29] Samoilenko, A.M., & Perestyuk, N.A. (1995). i.org/10.1007/978-0-387-21593-8
Impulsive differential equations. World Scientific [44] Hale, J.K., & Kato, J. (1978). Phase space for
Publishers, Singapore. https://doi.org/10.1 retarded equations with infinite delay. Funckcial.
142/9789812798664 Ekvac, 21, 11-41.
[30] Stamova, I. (2016) Applied impulsive mathemat- [45] Hino, Y., Murakami, S., & Naito, T. (1991).
ical models. Springer, International publishing, Functional differential equations with infinite
Switzerland. delay:Lecture notes in mathematics. Springer,
[31] Yue, C. (2014). Second-order neutral impulsive Berlin, Heidelberg.
stochastic evolution equation with infinite delay.
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