On solutions of a hybrid generalized Caputo-type problem via the noncompactness measure in the generalized version of Darbo's criterion

• Main Authors: Adjimi, Naas, Boutiara, Abdellatif, Samei, Mohammad Esmael, Etemad, Sina, Rezapour, Shahram, Kaabar, Mohammed K. A.
• Format: Article
• Published: Institute for Ionics 2023
• Subjects: QA Mathematics
• Online Access: http://eprints.um.edu.my/38571/

In this manuscript, we study the existence and uniqueness of solutions for a new neutral hybrid nonlinear differential equation in the context of a fractional generalized operator in the sense of psi-Caputo. To emphasize the novelty of the manuscript, a pure technique of the noncompactness measures is applied to a hybrid system based on the notion of the modulus of continuity in Darbo's criterion that covers the existing results of other works published before. The Ulam-Hyers and generalized Ulam-Hyers stabilities are explored for the given neutral nonhybrid nonlinear problem. An application is prepared in the framework of an example to ensure the validity of theorems for different cases.