Asymptotic Behavior of Mild Solutions of Some Fractional Functional Integro-differential Equations

Gisèle Mophou (1) , Gaston M. N'Guérékata (2, 1) , Vincent Valmorin (1)

1 CEREGMIA - Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée
2 Department of Mathematics, Morgan State University

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.

Mots clés: Integro-differential equation; mild solution; anti-periodicity

Domaines: Analyse fonctionnelle [math.FA]

Gisèle Mophou, Gaston M. N'Guérékata, Vincent Valmorin. Asymptotic Behavior of Mild Solutions of Some Fractional Functional Integro-differential Equations. African Diaspora Journal of Mathematics, 2013, 16 (1), pp.70-81. ⟨hal-01678067⟩