TY - JOUR
TI - Existence and stability theory of pantograph conformable fractional differential problem
AU - Sher Muhammad
AU - Khan Aziz
AU - Shah Kamal
AU - Abdeljawad Thabet
JN - Thermal Science
PY - 2023
VL - 27
IS - 101
SP - 237
EP - 244
PT - Article
AB - 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.