On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative

Fahd Jarad, Thabet Abdeljawad and Zakia Hammouch

Chaos, Solitons & Fractals, 2018, vol. 117, issue C, 16-20

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.

Keywords: Atangana–Baleanu fractional derivatives; Atangana–Baleanu fractional integrals; Gronwall inequality; Ulam–Hyers stability (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (41)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:117:y:2018:i:c:p:16-20

DOI: 10.1016/j.chaos.2018.10.006

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