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Abstract Cauchy problem for fractional differential equations. (English) Zbl 1268.34034

Summary: A generalized Darbo’s fixed-point theorem associated with Hausdorff measure of noncompactness is established. Then we apply this new variant fixed-point theorem to study some fractional differential equations in Banach spaces via the technique of measure of noncompactness. Many novel existence and uniqueness results for solutions are obtained under the more general conditions.

MSC:

34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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