RESUMEN

In this paper, we treat the fractional integral equation of the form

u(t) = u0 −1􀀀(_)Z t0(t − _)_−1[A(_)u(_) − f(_)]d_,

where 0 < _ _ 1, 􀀀(_) is the gamma function, {A(t) : t _ 0} is a familyof linear closed operators defined on a dense set D(A) in a Banach space E into E, u0 is an element of D(A) and f is a given E-valued function defined on an intervall [0, T]. The existence and uniqueness of the solution of the considerd integral equation is studied for a suitable class of the family of operators {A(t) : t_[0, T]}. The continuous dependence of solutions on f and u0 is also studied. An application is given to a mixed problem of general parbolic partial differential equations with fractional order.