Nonlocal Problems for Fractional Differential Equations via Resolvent Operators | Zendy

Zhenbin Fan | Zendy; Gisèle Mophou | Zendy

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Nonlocal Problems for Fractional Differential Equations via Resolvent Operators

Author(s) -

Zhenbin Fan,

Gisèle Mophou

Publication year - 2013

Publication title -

international journal of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 20

eISSN - 1687-9651

pISSN - 1687-9643

DOI - 10.1155/2013/490673

Subject(s) - resolvent , mathematics , lipschitz continuity , resolvent formalism , operator (biology) , compact space , mathematical analysis , cauchy distribution , differential (mechanical device) , lipschitz domain , pure mathematics , finite rank operator , banach space , biochemistry , chemistry , engineering , repressor , transcription factor , gene , aerospace engineering

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

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