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

Document Type : Research Paper


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


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.