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

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.

Keywords

• fractional differential equations
• analytic semigroup
• compact semigroup
• fixed point
• mild solution