Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China.
Chaos. 2023 Jan;33(1):013120. doi: 10.1063/5.0125651.
In this article, we consider conformable fractional stochastic differential equations (CFSDEs) driven by fBm with infinite delay via measures of noncompactness (MNC). As far as we know, there are few papers considering this issue. First, by virtue of a Mönch fixed point theorem and MNC, we explore the existence of solutions for CFSDEs. Subsequently, with the aid of Jensen inequality, Hölder inequality, stochastic analysis techniques, and semigroup theory, the controllability for this considered CFSDEs is investigated by employing a Mönch fixed point theorem. Thereafter, the controllability of CFSDEs with nonlocal conditions is discussed. Finally, the theoretical result is supported through an example.
在本文中，我们通过非紧测度（MNC）研究了无穷时滞的 fBm 驱动的相容分数阶随机微分方程（CFSDEs）。据我们所知，很少有论文考虑这个问题。首先，我们利用 Mönch 不动点定理和 MNC 来探讨 CFSDEs 解的存在性。随后，借助 Jensen 不等式、Hölder 不等式、随机分析技术和半群理论，利用 Mönch 不动点定理研究了该 CFSDEs 的可控性。此后，讨论了具有非局部条件的 CFSDEs 的可控性。最后，通过一个例子验证了理论结果。
