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

Abstract

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

Keywords

• fractional evolution equation with delay
• S-asymptotically periodic solutions
• existence and global asymptotic behavior
• C0-semigroup
• measure of noncompactness
• Gronwall-type inequality with delay