In this paper, we prove a new composition theorem for asymptotically antiperiodic and weighted pseudo antiperiodic functions. We also give some sufficient conditions to ensure invertibility of convolution operators in the space of antiperiodic functions. Then we prove the existence and uniqueness of asymptotically antiperiodic mild solutions to some fractional functional integro-differential equations in a Banach space using the Banach's fixed point theorem.
"Asymptotic Behavior of Mild Solutions of Some Fractional Functional Integro-differential Equations." Afr. Diaspora J. Math. (N.S.) 16 (1) 70 - 81, 2013.