Existence for Nonautonomous Fractional Integrodifferential Equations with Nonlocal Conditions

Abstract EN

We study the existence of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with nonlocal conditions in a separable Banach space X.

Combining the techniques of operator semigroup, noncompactness measures, and the fixed point theory, we obtain new existence of mild solution without the assumptions that the nonlinearity f satisfies a Lipschitz type condition and the semigroup {exp(−tA(s))} generated by {−A(s)}s∈[0,T] is compact.

An application of the abstract result is also given.