A New Generalized Gronwall Inequality with a Double Singularity and Its Applications to Fractional Stochastic Differential Equations. Issue 6 (2nd November 2019)

• Record Type: Journal Article
• Authors: Ding, Xiao-Li; Daniel, Cao-Labora; Nieto, Juan J.
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 6(2019)
• Page Start: 1042
• Page End: 1056
• Publication Date: 2019-11-02
• Subjects: Gronwall inequality -- fractional stochastic differential equations -- mild solutions; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1640612
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In many cases, the existence and uniqueness of the solution of a differential equation are proved using fixed point theory. In this paper, we utilize the theory of operators and ingenious techniques to investigate the well-posedness of mild solution to semilinear fractional stochastic differential equations. We first discuss some properties of a class of Volterra integral operators and then establish a new generalized Gronwall integral inequality with a double singularity. Finally, we use the properties and integral inequality to study the well-posedness of mild solution to the semilinear fractional stochastic differential equations. One sees that it is concise and effectiveness using the previous results to investigate the well-posedness of the mild solution.