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Axioms 2017, 6(4), 30; doi:10.3390/axioms6040030

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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Received: 5 October 2017 / Revised: 9 November 2017 / Accepted: 14 November 2017 / Published: 20 November 2017
(This article belongs to the Special Issue Fractional Differential Equations)
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Abstract

In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and fixed point theorems, with the help of some estimations. Examples are also given to illustrate the applicability of our results. View Full-Text
Keywords: fractional differential equations; analytic semigroup; compact semigroup; fixed point; mild solution fractional differential equations; analytic semigroup; compact semigroup; fixed point; mild solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liang, J.; Mu, Y. Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay. Axioms 2017, 6, 30.

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