Nonlocal Problems for Fractional Differential Equations via Resolvent Operators. (5th June 2013)

• Record Type: Journal Article
• Authors: Fan, Zhenbin; Mophou, Gisèle
• Other Names: Ntouyas Sotiris Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2013(2013)
• Publication Date: 2013-06-05
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2013/490673
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.