Abstract Cauchy problem for fractional differential equations
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In this paper, 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.
KeywordsFractional differential equations Cauchy problems Impulsive problems Nonlocal problems Hausdorff measure of noncompactness
The first author acknowledges the support by National Natural Science Foundation of China (11201091) and Key Projects of Science and Technology Research in the Chinese Ministry of Education (211169); the second author acknowledges the support by National Natural Science Foundation of China (11271309), Specialized Research Fund for the Doctoral Program of Higher Education (20114301110001) and Key Projects of Hunan Provincial Natural Science Foundation of China (12JJ2001) and the third author acknowledges the support by Grants VEGA-MS 1/0507/11, VEGA-SAV 2/0124/10 and APVV-0414-07.
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