Mild Solution to Fractional Boundary Value Problem with Nonlinear Boundary Conditions

In this paper, we consider a system of boundary value problems for fractional differential equation given by { ( ) ( ) ( ( )) ? ( ) ( ( )) [ ] ( ) ( ) ( ( )) ( ) ( ( )) ( ) ( ) where is Caputoʹs fractional derivative of order , ( ) is a sectorial operator of type ( ) on a Banach space X ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) are bounded function, the functions are given operators satisfying some assumptions and is a integrable function on I. Several existence results of mild solutions are obtained.