SOME NEW RESULTS OF INITIAL BOUNDARY PROBLEM CONTAIN ABC-FRACTIONAL DIFFERENTIAL EQUATIONS OF ORDER α∈(2,3)

Abstract

The purpose of this research is to investegate the existence and uniqueness of solutions for a new class of Atangana-Baleanu fractional differential equations of order with periodic boundary conditions. Our results are based on the fixed points of Schauder, and Banach. In addition, investigate the stability of the solution using the Hyers-Ulam stable. Finally, presented an example to satisfy all theorems studies.MSC 2010: 34A08, 26A33, 34G20, 34C25, 45J05