A note on the continuity for Caputo fractional stochastic differential equations

Wenya Wang; Shuilin Cheng; Zhongkai Guo; Xingjie Yan

doi:10.1063/1.5141485

A note on the continuity for Caputo fractional stochastic differential equations

Chaos. 2020 Jul;30(7):073106. doi: 10.1063/1.5141485.

Authors

Wenya Wang¹, Shuilin Cheng², Zhongkai Guo³, Xingjie Yan⁴

Affiliations

¹ School of Mathematics and Computer Science, Jianghan University, Wuhan 430056, China.
² School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430074, China.
³ School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China.
⁴ Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China.

PMID: 32752624
DOI: 10.1063/1.5141485

Abstract

The first aim of this paper is to establish the well-posedness for a type of Caputo fractional stochastic differential equations, and we obtain the global existence and uniqueness of solutions under some conditions consistent with the classic (integer order) stochastic differential equations. The second aim is that we consider the continuity of solutions on the fractional order of those equations.