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

By Fahd Jarad, Thabet Abdeljawad, Zakia Hammouch. Chaos, Solitons & Fractals, 2018

323 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/77fce1f8bf3db1835d38afa95b3dbc92f0a483a3

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Analysis of some generalized ABC – Fractional logistic models (2019, background): “After this derivative had been proposed, most of the works treated by the traditional fractional derivative were reconsidered by the new approach [19, 20].”
Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel (2019, background): “Thus, with the help of (34) to (36), the functions i,n(t) → 0, as n → ∞ for i = 1, 2, 3 with λ < 1, which completes the proof.”