分数阶随机微分方程解的存在性与唯一性  

Existence and Uniqueness of Solutions for Fractional Stochastic Differential Equations

作　　者：罗欢 陈付彬[1] 周旋[1] LUO Huan;CHEN Fubin;ZHOU Xuan(Kunming University of Science and Technology Oxbridge College,Kunming 650106,China)

机构地区：[1]昆明理工大学津桥学院,云南昆明650106

出　　处：《贵州大学学报（自然科学版）》2023年第2期24-28,共5页Journal of Guizhou University:Natural Sciences

基　　金：云南省教育厅科学研究基金资助项目(2020J1233,2022J1098)。

摘　　要：研究了一类分数阶随机微分方程解的存在性与唯一性。通过运用微分方程的半离散化技术,推导出分数阶随机微分方程解的半离散化模型,利用Minkowski不等式、Holder不等式和Picard逐步逼近法,证明了半离散随机模型解的存在性与唯一性。In this paper,the existence and uniqueness of solutions for a class of fractional stochastic differential equations are studied.By using the semi-discretization technique of differential equations,the semi-discretization model for solutions of fractional stochastic differential equations is derived and then the existence and uniqueness of solutions of semi-discretization stochastic differential equations are proved by using Minkowski inequality,Holder inequality and Picard approximation method.

关 键 词：分数阶 Picard迭代 Mittag-Leffler函数 

分 类 号：O175.1[理学—数学]