New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative. (November 2019)

• Record Type: Journal Article
• Authors: Gao, Wei; Ghanbari, Behzad; Baskonus, Haci Mehmet
• Is Part Of: Chaos, solitons and fractals. Volume 128(2019)
• Page Start: 34
• Page End: 43
• Publication Date: 2019-11
• Subjects: Computational method -- Fractional derivative -- Differential operator; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.07.037
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this work, we introduce ABC-Caputo operator with ML kernel and its main characteristics are discussed. Viral diseases models for AIDS and Zika are considered, and finally, as third model, the macroeconomic model involving ABC fractional derivatives is investigated, respectively. It is presented that the AB Caputo derivatives satisfy the Lipschitz condition along with superposition property. The numerical methods for solving the fractional models are presented by means of ABC fractional derivative in a detailed manner. Finally the simulation results obtained in this paper according to the suitable values of parameters are also manifested.