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

被引：71
作者：
Singh, Ajeet [1 ]
Shukla, Anurag [1 ]
Vijayakumar, V. [2 ]
Udhayakumar, R. [2 ]
机构：
[1] Rajkiya Engn Coll Kannauj, Dept Appl Sci, Kannauj 209732, India
[2] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore 632014, Tamil Nadu, India
来源：
CHAOS SOLITONS & FRACTALS | 2021年 / 150卷
关键词：
Fractional differential equations; Stochastic system; Stability; Mild solution; Sine and cosine family of functions; APPROXIMATE CONTROLLABILITY; EXISTENCE; SYSTEMS; UNIQUENESS;
D O I：
10.1016/j.chaos.2021.111095
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1 < alpha < 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. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：9
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