Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 155, pp. 1-7.

Title: Existence and uniqueness of solutions to fractional semilinear 
       mixed Volterra-Fredholm integrodifferential equations with 
       nonlocal conditions
       
Author: Mohammed M. Matar Al-Azhar (Univ. of Gaza, Palestine)

Abstract:
 In this article we study the fractional semilinear mixed
 Volterra-Fredholm integrodifferential equation
 $$
 \frac{d^{\alpha }x(t)}{dt^{\alpha }} =Ax(t)+f\Big(t,x(t),
 \int_{t_0}^tk(t,s,x(s))ds,\int_{t_0}^{T}h(t,s,x(s))ds\Big) ,
 $$
 where $t\in [t_0,T]$, $t_0\geq 0$, $0<\alpha <1$, and $f$
 is a given function. We prove the existence and uniqueness
 of  solutions to this equation, with a nonlocal condition.
 
Submitted September 12, 2009. Published December 01, 2009.
Math Subject Classifications: 45J05, 26A33, 34A12.
Key Words: Fractional integrodifferential equations;
    mild solution; nonlocal condition; Banach fixed point.