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Cauchy problem for fractional evolution equations with Caputo derivative
Journal article   Peer reviewed

Cauchy problem for fractional evolution equations with Caputo derivative

Y. Zhou, X. H. Shen and L. Zhang
The European physical journal. ST, Special topics, Vol.222(8), pp.1749-1765
01/09/2013
DOI: https://doi.org/10.1140/epjst/e2013-01961-5

Abstract

Physical Sciences Physics Physics, Multidisciplinary Science & Technology
This paper concerns the abstract nonlocal Cauchy problem of a class of fractional evolution equations with Caputo derivative. A suitable mild solution of evolution equations with Caputo derivative is introduced. In the cases C (0) semigroup is compact or noncompact, the existence theorems of mild solutions for the nonlocal Cauchy problem are established by means of fractional calculus, theory of Hausdorff measure of noncompactness and fixed point theorems.

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