Existence of mild solutions for fractional evolution equations

Abstract

In this paper, we study the nonlocal Cauchy problems of fractional evolution equations with Riemann-Liouville derivative by considering an integral equation which is given in terms of probability density. By using the theory of Hausdorffmeasure of noncompactness, we establish various existence theorems of mild solutions for the Cauchy problems in the cases C0 semigroup is compact or noncompact. © 2013 Rocky Mountain Mathematics Consortium.