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Stability of a Non-Lipschitz Stochastic Riemann-Liouville Type Fractional Differential Equation Driven by Lévy Noise

Guangjun Shen, Jiang-lun Wu, Ruidong Xiao, Weijun Zhan

Acta Applicandae Mathematicae, Volume: 180, Issue: 1

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s10440-022-00506-w

Abstract

In this paper, stability of a non-Lipschitz stochastic Riemann-Liouville type fractional differential equation driven by L\'levy noise is studied. Three types of stability, namely, stochastic stability, almost sure exponential stability, and moment exponential stability, of the fractional equat...

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Published in: Acta Applicandae Mathematicae
ISSN: 0167-8019 1572-9036
Published: Springer Nature Switzerland AG Springer Science and Business Media LLC 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa60140
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Abstract: In this paper, stability of a non-Lipschitz stochastic Riemann-Liouville type fractional differential equation driven by L\'levy noise is studied. Three types of stability, namely, stochastic stability, almost sure exponential stability, and moment exponential stability, of the fractional equation are established. Examples are given to illustrate and to support our results.
Keywords: Fractional derivative of Riemann-Liouville type · Stochastic fractional differential equations with non-Lipschitz coefficients · Lévy noise · Stochastic stability · Almost sure exponential stability · Moment exponential stability
College: Faculty of Science and Engineering
Funders: This research was supported by the National Natural Science Foundation of China (12071003). This research was also supported by the Top Talent Project of University Discipline (speciality) (gxbjZD03) and by the National Natural Science Foundation of China (11901005).
Issue: 1

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