On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

Mathematics

Seyfeddine Moualkia¹  Yong Xu¹ 

[1] School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China;

关键词: fractional stochastic differential equations;    variable order;    existence and uniqueness;   

DOI  :  10.3390/math9172106

来源: DOAJ

【 摘 要 】

Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.

【 授权许可】

Unknown