Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

Year 2020, Volume: 4 Issue: 4, 349 - 360, 30.12.2020

Choukri Derbazi , Zidane Baitiche Mouffak Benchohra

https://doi.org/10.31197/atnaa.706292

Cited By: 5

Abstract

This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the $\psi $--Caputo fractional derivative in Banach spaces. Our approach is based on a new fixed point theorem with respect to convex-power condensing operator combined with the technique of measures of noncompactness. Finally, two examples are given to illustrate the obtained results.                                                                                                                                                                                                                                                                                                                      

Keywords

$\psi $--Caputo fractional derivative, Cauchy problem, convex-power condensing operator, fixed point theorem, Banach spaces, measures of noncompactness

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