Existence of Solutions to Fractional Mixed Integrodifferential Equations with Nonlocal Initial Condition

We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition d(alpha)x(t)/dt(alpha) = f(t,x(t), integral t,s,x(s))ds, x(0) = integral(1)(0) g(s)x(s)ds, where t is an element of [0, 1], 0 < alpha < 1, and f is a given function. We point out that such a kind of initial conditions or nonlocal restrictions could play an interesting role in the applications of the mentioned model. The results obtainded are applied to an example.