Jarad, FahdJarad, FahdAbdeljawad, ThabetAbdeljawad, ThabetHammouch, Zakia2020-03-172020-03-172018Jarad, Fand; Abdeljawad, Thabet; Hammouch, Zakia, "On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative", Chaos Solitons & Fractals, Vol. 117, pp. 16-20, (2018).0960-0779https://hdl.handle.net/20.500.12416/2657In this paper, we discuss the conditions of existence and uniqueness of solutions to a certain class of ordinary differential equations involving Atangana-Baleanu fractional derivative. Benefiting from the Gronwall inequality in the frame of Riemann-Liouville fractional integral, we establish a Gronwall inequality in the frame of Atangana-Baleanu fractional integral. Then, we study the stability of such equations in the sense of Ulam. (C) 2018 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessAtangana-Baleanu Fractional DerivativesAtangana-Baleanu Fractional IntegralsGronwall InequalityUlam-Hyers StabilityArticle117162010.1016/j.chaos.2018.10.006