Optimal (ω,c)-asymptotically periodic mild solutions to some fractional evolution equations

Abstract

In this article, we establish some new properties of the two-parameter Mittag-Leffler function and use them to prove that, mild solutions of the evolution equation) -asymptotically periodic, where A is the generator of a strongly continuous semigroup {T ( )}  0 (which is exponentially stable) on a Banach space X and C D  t denotes the Caputo fractional derivative of order 0 <  1 . We further establish an existence and uniqueness result for optimal (,c) -asymptotically periodic mild solution if X is a uniformly convex Banach space.