The paper deals with the existence and uniqueness of mild solutions to a semilinear integro-differential equation of fractional order. The problem studied here is:
where , is the infinitesimal generator of a noncompact and analytic semigroup on a Banach space and and some functions. The initial data is taken from the Banach space , with with the norm . Under various conditions on the functions and , the above problem admits a unique mild solution. The main techniques employed here are the Banach contraction principle and a fixed point theorem.