On the oscillation of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel. (October 2019)

• Record Type: Journal Article
• Authors: Abdalla, Bahaaeldin; Abdeljawad, Thabet
• Is Part Of: Chaos, solitons and fractals. Volume 127(2019)
• Page Start: 173
• Page End: 177
• Publication Date: 2019-10
• Subjects: Mittag–Leffler -- Nonsingular kernel -- Fractional differential equations -- Oscillation theory; 34A08 -- 34C10 -- 26A33; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.07.001
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this article, we derive sufficient conditions to prove the oscillation for solutions of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel of the form { ( a A B C D κ 0 ξ ) ( t ) + ϕ 1 ( t, ξ ) = θ ( t ) + ϕ 2 ( t, ξ ), t > a ξ k ( a ) = b k ( k = 0, 1, …, n ), where n < κ 0 ≤ n + 1 and a A B C D κ 0 is the left-fractional Caputo derivative with Mittag–Leffler nonsingular kernel or the Atangana–Baleanu fractional derivative in the sense of Caputo. An example is given to validate part of the proven results.