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Abstract and Applied Analysis
Volume 2016, Article ID 4567092, 15 pages
Research Article

Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

Received 7 July 2016; Accepted 22 August 2016

Academic Editor: Khalil Ezzinbi

Copyright © 2016 Rodrigo Ponce. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases and