Abstract
We first prove the existence, uniqueness and continuous dependence of mild solutions to stochastic delay evolution equations with a Caputo fractional derivative:DtαCy(t)=Ay(t)+f(t,yt)+g(t,yt)dW(t)dt,12<α<1. Then, we investigate the asymptotic behavior of mild solutions to fractional stochastic delay evolution equations of the formDtαCy(t)=Ay(t)+It1−αf(t,yt)+[It1−αg(t,yt)]dW(t)dt,0<α<1. In particular, the existence of a global forward attracting set in the mean-square topology is established. A general theorem on the existence of mild solutions is obtained by using α-order fractional resolvent operator theory and the Schauder fixed point theorem.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
