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

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in L^p([۰,۱],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:

Semilinear integro-differential fractional equations , Measure of noncompactness , Mild solutions , Schauder fixed point theorem , Darbo fixed point theorem