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

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 <inline-formula> <math display="inline"> <semantics>...

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Bibliographic Details
Main Author: He Yang
Format: Article
Language:English
Published: MDPI AG 2020-06-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/12/6/1031
Description
Summary: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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>∈</mo> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-order Riemann–Liouville fractional stochastic evolution equations of Sobolev type in abstract spaces. Then the symmetrical technique is used to deal with the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>∈</mo> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-order Caputo fractional stochastic evolution equations of Sobolev type in abstract spaces. Two examples are given as applications to the obtained results.
ISSN:2073-8994