On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative
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2018
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Pergamon-Elsevier Science LTD
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Abstract
In 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.
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Atangana-Baleanu Fractional Derivatives, Atangana-Baleanu Fractional Integrals, Gronwall Inequality, Ulam-Hyers Stability
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Jarad, 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).
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Chaos Solitons & Fractals
Volume
117
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16
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20