- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces
Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces
Authors : Choukri DERBAZİ, Zidane BAİTİCHE, Mouffak BENCHOHRA
Pages : 349-360
Doi:10.31197/atnaa.706292
View : 5 | Download : 9
Publication Date : 2020-12-30
Article Type : Research
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