# $L^p$-existence of mild solutions of fractional differential equations in Banach space

Document Type : Research Paper

Author

Carthage University, Department of Mathematics, Bizerte Preparatory Engineering Institute, Tunisia

Abstract

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in
$L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of
noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.

Keywords

### History

• Receive Date: 05 February 2018
• Revise Date: 09 June 2018
• Accept Date: 15 December 2018