Title APPLICATIONS OF α − φ-GERAGHTY FOR THE EXISTENCE RESULTS IN A BOUNDARY VALUE PROBLEM WITH THE MITTAG-LEFFLER KERNEL Type of Research Article Keywords Atangana-Baleano fractional Differential Operator,Fractional Differential Equations, Boundary Value Problems, Abstract This research studies some important conditions for the existence of a solution for a boundary value problem with the Mittag-Leffler kernel. Our results are based on α − φ-Geraghty type contractive mapping. Researchers Rana Akbari (First Researcher)، Hojjat Afshari (Second Researcher)، asghar ahmadkhanlu (Third Researcher)