Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations
type: Item
instance of: scholarly article
title: Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations
zbMATH Open document ID: 1243.34006
author: P. Revathi
author: Selvaraj Marshal Anthoni
author: R. Sakthivel
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2012-03-22T00:00:00Z
review text: This paper is concerned with the existence and uniqueness of square-mean pseudo almost automorphic (mild) solutions for a class of fractional stochastic differential equations in a Hilbert space. The authors have used stochastic analysis and fixed point theory to get their results. This paper is well written and it is nice to read. From an applied perspective it is of great significance to introduce stochastic effects in the investigation of fractional differential equations and develop a study of type of periodicity and ergodicity for these equations. Such subject is one of most interesting topics in the theory of evolution equations both due to its theoretical interest as well as due to their concrete applications. We observe that the existence of almost automorphic, pseudo-almost periodic and pseudo-almost automorphic solutions to fractional differential equations has been considered only in a few publications. Some complementary references to this paper are the following: \textit{R. P. Agarwal}, \textit{B. de Andrade} and \textit{C. Cuevas}, ``On type of periodicity and ergodicity to a class of fractional order differential equations'', Adv. Difference Equ. 2010, Article ID 179750, 25 p. (2010; Zbl 1194.34007). \textit{R. P. Agarwal}, \textit{B. de Andrade} and \textit{C. Cuevas}, ``Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations'', Nonlinear Anal., Real World Appl. 11, No. 5, 3532--3554 (2010; Zbl 1248.34004). \textit{C. Cuevas}, \textit{G. N'Guérékata} and \textit{A. Sepulveda},``Pseudo almost automorphic solutions to fractional differential and integro-differential equations'', Commun. Appl. Anal. 16, No. 1, 131--152 (2012). \textit{C. Cuevas}, \textit{H. Soto} and \textit{A. Sepulveda}, ``Almost periodic and pseudo-almost periodic solutions to fractional differential and integro-differential equations'', Appl. Math. Comput. 218, No. 5, 1735--1745 (2011; Zbl 1246.45012).
reviewed by: Claudio Cuevas
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 43A60
zbMATH DE Number: 6017579
zbMATH Keywords: fractional stochastic differential equation
zbMATH Keywords: existence result
zbMATH Keywords: square-mean pseudo almost automorphic
zbMATH Keywords: mild solution
MaRDI profile type: Publication
full work available at URL: j.na.2011.12.028
OpenAlex ID: W2080771073
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DOI: 10.1016/J.NA.2011.12.028
description: scientific article; zbMATH DE number 6017579