## Topological Methods in Nonlinear Analysis

### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 42, Number 1 (2013), 119-136.

Dates
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.tmna/1461247296

Mathematical Reviews number (MathSciNet)
MR3155618

Zentralblatt MATH identifier
1292.34075

#### Citation

Zhou, Yong; Jiao, Feng; Pečarić, Josip. Abstract Cauchy problem for fractional functional differential equations. Topol. Methods Nonlinear Anal. 42 (2013), no. 1, 119--136. https://projecteuclid.org/euclid.tmna/1461247296

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