Existence and stability theory of pantograph conformable fractional differential problem

Abstract

The purpose of this paper is to investigate the existence and uniqueness (EU) of solutions to a class of conformable fractional differential equations (DE) with delay term using Krasnoselskii's fixed point theorem. The proposed problem is devoted to non-local initial value problems. Such problems are increasingly occurred in applications like in the filed of quantum mechanics and electrodynamics. The theoretical analysis is further enriched by establishing stability theory due to Ulam and its different kinds including ?Ulam-Hyers (UH), generalized Ulam-Hyers (GUH), Ulam-Hyers-Rassias (UHR), and generalized Ulam-Hyers-Rassias (GUHR)? stability for the considered class. The obtain analysis is then testified by an example.