Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations. (26th October 2019)

• Record Type: Journal Article
• Authors: Yan, Zuomao; Jia, Xiumei
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 14(2019)
• Page Start: 1593
• Page End: 1643
• Publication Date: 2019-10-26
• Subjects: Analytic α-resolvent operator -- fixed point -- fractional impulsive neutral stochastic functional integro-differential equations -- infinite delay -- optimal solutions; 34A37 -- 60H10 -- 34G25 -- 26A33 -- 93E20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1501060
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α -resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.