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Open AccessArticle

Existence Results of Mild Solutions for the Fractional Stochastic Evolution Equations of Sobolev Type

by He Yang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Symmetry 2020, 12(6), 1031; https://doi.org/10.3390/sym12061031
Received: 29 May 2020 / Revised: 14 June 2020 / Accepted: 17 June 2020 / Published: 19 June 2020
(This article belongs to the Special Issue Advances in Stochastic Differential Equations)
In this paper, by utilizing the resolvent operator theory, the stochastic analysis method and Picard type iterative technique, we first investigate the existence as well as the uniqueness of mild solutions for a class of α ( 1 , 2 ) -order Riemann–Liouville fractional stochastic evolution equations of Sobolev type in abstract spaces. Then the symmetrical technique is used to deal with the α ( 1 , 2 ) -order Caputo fractional stochastic evolution equations of Sobolev type in abstract spaces. Two examples are given as applications to the obtained results. View Full-Text
Keywords: fractional resolvent family; existence and uniqueness; fractional stochastic evolution equations; Picard’s iteration technique fractional resolvent family; existence and uniqueness; fractional stochastic evolution equations; Picard’s iteration technique
MDPI and ACS Style

Yang, H. Existence Results of Mild Solutions for the Fractional Stochastic Evolution Equations of Sobolev Type. Symmetry 2020, 12, 1031.

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