Existence of mild solutions for semilinear $\psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces

Year 2022, Volume: 5 Issue: 4, 459 - 472, 30.12.2022

Ali El Mfadel , Fatima Ezzahra Bourhim , M'hamed Elomari

https://doi.org/10.53006/rna.1121916

Cited By: 5

https://izlik.org/JA84ZN22GT

Abstract

The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.

Keywords

$\psi-$fractional integral , $\psi-$Caputo fractional derivative , fixed point , compact semigroup

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