Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 240, pp. 1-14.

Title: Solutions to nonlocal fractional differential equations using
       a noncompact semigroup

Authors: Shaochun Ji (Huaiyin Institute of Technology, Huaian, China)
         Gang Li  (Yangzhou University, Yangzhou, China}

Abstract:
 This article concerns the existence of solutions to nonlocal fractional
 differential equations in Banach spaces. By using a type of
 newly-defined measure of noncompactness, we discuss this problem
 in general Banach spaces without any compactness assumptions to
 the operator semigroup. Some existence results are obtained when
 the nonlocal term is compact and when is Lipschitz continuous.

Submitted August 22, 2013. Published October 29, 2013.
Math Subject Classifications: 26A33, 34G20.
Key Words: Fractional differential equations;
           nonlocal conditions;  measure of noncompactness.