Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay

This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study existence mild solutions under situation that relevant semigroup is and nonlinear term satisfies more general growth conditions instead Lipschitz-type conditions. Moreover, by establishing Gronwall-type integral inequality corresponding to differential delay, consider global asymptotic behavior solutions, which will make up for blank this field.