Volume 45_4_(2024)_229-244

Existence and uniqueness results for nonlinear hybrid Ψ-Caputo-type fractional differential equations with nonlocal periodic boundary conditions
Fatima Ezzahra Bourhim, Ali El Mfadel, M'hamed Elomari, Naoufel Hatime

Abstract. In this paper, we consider a nonlinear fractional hybrid differential equation involving the Ψ-Caputo fractional operator with nonlocal periodic boundary conditions. Based on Lipschitz and Carathéodory conditions and via the Krasnoselskii fixed point theorem and some basic fractional analysis techniques, we discuss the existence and uniqueness of solutions to the proposed problem. Moreover, for a specific class of continuous functions, we prove some fundamental fractional differential inequalities. We finish this work with a non-trivial example

Rend. Mat. Appl. (7) 45 (2024) 229-244;  pdf