On some fractional evolution equation with nonlocal conditions

Mahmoud Mohammed Mostafa El-Borai Alexandria University, Egypt

In this paper, Leray-Schauder principle is used to establish existence results for the nonlocal initial value problem of the following type

\frac{d^{α}u(t)}{dt^{α}} = Au(t) + f(t, B(t)u), t > 0

u(0) = u_{o} + g(u).

Here 0 < α ≤ 1, A is the infinitesimal generator of a strongly continuous semigroup of bounded operators Q(t) in the Banach space E, {B(t) : t > 0 is a family of linear closed operator defined on a dense set in E into E and f, g are given E-valued functions.