ON THE EXISTENCE OF MILD SOLUTIONS FOR A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS IN THE α-NORM

摘要

This paper concerns the existence of mild solutions for some fractional Cauchy problem with nonlocal conditions in the α-norm. The linear part of the equations is assumed to generate an analytic compact bounded semigroup, and the nonlinear part satisfies some Lipschitz conditions with respect to the fractional power norm of the linear part. By using a fixed point theorem of Sadovskii, we establish some existence results which generalize ones in the case of fractional order derivative.