Existence of solutions of the abstract Cauchy problem of fractional order (Q831106)

In this work, authors consider a fractional abstract Cauchy problem. The operator is assumed to be a closed linear operator and the forcing term assumed to be in an appropriate space of X-valued functions. The order of the derivative is taken between one and two. The aim is to study the differentiability of mild solutions. To obtain the results, the concept of alpha-resolvent family is used extensively. The existence of classical solution is shown using the regularity properties of such family. The paper contains very interesting results which may be useful for further studies.