On a Class of Ordinary Differential Equations in the Frame of Atangana-Baleanu Fractional Derivative
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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.
Description
Hammouch, Zakia/0000-0001-7349-6922; Jarad, Fahd/0000-0002-3303-0623
Keywords
Atangana-Baleanu Fractional Derivatives, Atangana-Baleanu Fractional Integrals, Gronwall Inequality, Ulam-Hyers Stability, Atangana–Baleanu Fractional Derivatives, Ulam–Hyers Stability, Atangana–Baleanu Fractional Integrals, Gronwall inequality, Atangana-Baleanu fractional integrals, Fractional ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Stability of solutions to ordinary differential equations, Atangana-Baleanu fractional derivatives, Ulam-Hyers stability
Fields of Science
0103 physical sciences, 01 natural sciences
Citation
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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307
Volume
117
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16
End Page
20
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Scopus : 350
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