Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces

Ajeet Singh, Anurag Shukla, V. Vijayakumar and R. Udhayakumar

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1<α≤2. We have considered the family of stochastic differential equations with variable delay in the state. For proving our main results, we apply the Banach fixed point theorem and imposed the Lipschitz condition on nonlinearity. Finally, we present an example to illustrate the obtained theory.

Keywords: Fractional differential equations; Stochastic system; Stability; Mild solution; Sine and cosine family of functions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004495

DOI: 10.1016/j.chaos.2021.111095

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