Existence and Uniqueness of Continuous Solutions of Fractional Mixed Type Integrodifferential Equations in Cone-Metric Spaces

Abstract

In this paper we investigate the existence and uniqueness for the fractional mixed type integro-differntial equations and the existence of unique common solution of the Urysohn integral equations in cone metric spaces. The result is obtained by using the some extensions of Banach’s contraction principle, common fixed points for two self-mappings in complete cone metric space and the theory of cosine family.

Keywords: Cone metric space, Cosine family, fixed point, Contractive mapping, Ordered Banach space.