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Global attractiveness and exponential stability for impulsive fractional neutral stochastic evolution equations driven by fBm
- Source :
- Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-17 (2020)
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- This paper is concerned with a class of fractional neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion (fBm). First, by means of the resolvent operator technique and contraction mapping principle, we can directly show the existence and uniqueness result of mild solution for the aforementioned system. Then we develop a new impulsive-integral inequality to obtain the global attracting set and pth moment exponential stability for this type of equation. Worthy of note is that this powerful inequality after little modification is applicable to the case with delayed impulses. Moreover, sufficient conditions which guarantee the pth moment exponential stability for some pertinent systems are stated without proof. In the end, an example is worked out to illustrate the theoretical results.
- Subjects :
- Global attracting set
Caputo fractional derivative
Algebra and Number Theory
Fractional Brownian motion
Partial differential equation
lcsh:Mathematics
Applied Mathematics
010102 general mathematics
Type (model theory)
lcsh:QA1-939
Exponential stability
Fractional neutral stochastic integro-differential equations
01 natural sciences
010101 applied mathematics
Moment (mathematics)
Delayed impulses
Ordinary differential equation
Applied mathematics
Contraction mapping
Uniqueness
0101 mathematics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 16871847
- Volume :
- 2020
- Database :
- OpenAIRE
- Journal :
- Advances in Difference Equations
- Accession number :
- edsair.doi.dedup.....25fe28ed5e00879c2f1bbc20e839fbe4