Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay. (English) Zbl 1356.34079
This paper is mainly concerned with an implusive neutral functional differential equation driven by a fractional Brownian motion with infinite delay. Local and global existence and attractivity of mild solutions to this kind of equation has been established.
Reviewer: Yong-Kui Chang (Xi’an)
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K40 | Neutral functional-differential equations |
Keywords:
fractional Brownian motion; fixed point; mild solutions; attractivity; neutral stochastic functional differential equationReferences:
| [1] | Bainov DD, Systems with impulsive effect (1989) |
| [2] | DOI: 10.1155/9789775945501 · doi:10.1155/9789775945501 |
| [3] | DOI: 10.1515/9783110295313 · Zbl 1285.34002 · doi:10.1515/9783110295313 |
| [4] | DOI: 10.1016/j.camwa.2012.03.013 · Zbl 1268.34159 · doi:10.1016/j.camwa.2012.03.013 |
| [5] | DOI: 10.1016/j.cnsns.2013.07.011 · doi:10.1016/j.cnsns.2013.07.011 |
| [6] | DOI: 10.1016/j.jfranklin.2014.04.008 · Zbl 1395.93566 · doi:10.1016/j.jfranklin.2014.04.008 |
| [7] | DOI: 10.1016/j.amc.2012.12.033 · Zbl 1297.34082 · doi:10.1016/j.amc.2012.12.033 |
| [8] | DOI: 10.1142/9789812798664 · doi:10.1142/9789812798664 |
| [9] | DOI: 10.1142/0906 · doi:10.1142/0906 |
| [10] | DOI: 10.1007/BF02843536 · Zbl 0934.45012 · doi:10.1007/BF02843536 |
| [11] | Benchohra M, Mem. Differ. Equ. Math. Phys 25 pp 105– (2002) |
| [12] | DOI: 10.1016/j.camwa.2011.01.027 · Zbl 1217.60054 · doi:10.1016/j.camwa.2011.01.027 |
| [13] | Hale JK, Rev. Roum. Math. Pures Appl 39 pp 339– (1994) |
| [14] | DOI: 10.1016/j.jmaa.2003.11.052 · Zbl 1056.45012 · doi:10.1016/j.jmaa.2003.11.052 |
| [15] | DOI: 10.1016/j.spl.2012.04.013 · Zbl 1248.60069 · doi:10.1016/j.spl.2012.04.013 |
| [16] | DOI: 10.1007/s11464-013-0300-3 · Zbl 1279.60078 · doi:10.1007/s11464-013-0300-3 |
| [17] | DOI: 10.1080/00411450.2014.910813 · Zbl 1302.82082 · doi:10.1080/00411450.2014.910813 |
| [18] | DOI: 10.1080/07362994.2014.981641 · Zbl 1327.35460 · doi:10.1080/07362994.2014.981641 |
| [19] | DOI: 10.1002/mma.2967 · Zbl 1304.60069 · doi:10.1002/mma.2967 |
| [20] | DOI: 10.1007/s11464-015-0392-z · Zbl 1328.60140 · doi:10.1007/s11464-015-0392-z |
| [21] | Hale JK, Funkcial. Ekvac 21 pp 11– (1978) |
| [22] | DOI: 10.1002/mana.19981890103 · Zbl 0896.47042 · doi:10.1002/mana.19981890103 |
| [23] | DOI: 10.1007/s00440-003-0282-2 · Zbl 1036.60056 · doi:10.1007/s00440-003-0282-2 |
| [24] | Alos E, Ann. Probab 29 pp 766– (1999) |
| [25] | DOI: 10.1007/978-3-540-75873-0 · Zbl 1138.60006 · doi:10.1007/978-3-540-75873-0 |
| [26] | Nualart D, The Malliavin calculus and related topics, 2. ed. (2006) · Zbl 1099.60003 |
| [27] | DOI: 10.1016/j.na.2011.02.047 · Zbl 1218.60053 · doi:10.1016/j.na.2011.02.047 |
| [28] | DOI: 10.1007/978-1-4612-5561-1 · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1 |
| [29] | DOI: 10.1016/j.na.2009.10.021 · Zbl 1197.45005 · doi:10.1016/j.na.2009.10.021 |
| [30] | DOI: 10.1007/s00020-010-1767-x · Zbl 1198.45009 · doi:10.1007/s00020-010-1767-x |
| [31] | DOI: 10.1016/S0362-546X(99)00417-4 · Zbl 0995.34053 · doi:10.1016/S0362-546X(99)00417-4 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
