### Abstract Cauchy problem for fractional functional differential equations

#### Abstract

In this paper, the existence

and continuation of solutions for the Cauchy initial value problem

of fractional functional differential equations in an arbitrary

Banach space is discussed under hypotheses based on Carathéodory condition and the measure of noncompactness. In

addition, an example is given to show that the criteria on existence

of solutions for the initial value problem of fractional

differential equations in finite-dimensional spaces may not be true

in infinite-dimensional cases.

and continuation of solutions for the Cauchy initial value problem

of fractional functional differential equations in an arbitrary

Banach space is discussed under hypotheses based on Carathéodory condition and the measure of noncompactness. In

addition, an example is given to show that the criteria on existence

of solutions for the initial value problem of fractional

differential equations in finite-dimensional spaces may not be true

in infinite-dimensional cases.

#### Keywords

Fractional functional differential equations; Banach spaces; measure of noncompactness; existence; continuation

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