Nonlocal Problems for Fractional Differential Equations via Resolvent Operators

Zhenbin Fan and Gisèle Mophou

International Journal of Differential Equations, 2013, vol. 2013, 1-9

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:490673

DOI: 10.1155/2013/490673

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