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Romario FOKO TIOMELA (LAMIA) : Optimal (w,c)-Asymptotically Periodic Mild Solutions to some Fractional Evolution Equations.
We establish new properties of the two-parameter Mittag-Leffler function which we then use to prove that the mild solutions of some classes of fractional differential equations (with the Caputo fractional derivative) subject to the generator of a strongly continuous semigroup are (w,c)-asymptotically periodic in a Banach space X. We further establish an existence and uniqueness result for optimal (w,c)-asymptotically periodic mild solutions when the Banach space X is uniformly convex.