Time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by Gaussian white noise. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Liang, Jiarui; Shen, Tianlong; Qian, Xu; Song, Songhe
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 2(2019)
• Page Start: 123
• Page End: 136
• Publication Date: 2019-03-04
• Subjects: Caputo-type time fractional derivative -- fractional Laplacian operator -- Mittag–Leffler functions -- mild solution; 35Q99 -- 60H15; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2018.1486203
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We present the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein–Ulenbeck equations by the generalized Mittag–Leffler functions and Mainardi function, and establish the existence and uniqueness of mild solutions for time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by Gaussian white noise. In addition, the global mild solution is also shown.