A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel. (January 2020)

• Record Type: Journal Article
• Authors: Ganji, R.M.; Jafari, H.; Baleanu, D.
• Is Part Of: Chaos, solitons and fractals. Volume 130(2020)
• Publication Date: 2020-01
• Subjects: Fractional derivative -- Atangana-Baleanu-Caputo derivative -- Multi variable order -- The fifth-kind Chebyshev polynomials -- Collocation method; 34A08 -- 65N35; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109405
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper we consider multi variable orders differential equations (MVODEs) with non-local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of variable order. We use the fifth-kind Chebyshev polynomials as basic functions to obtain operational matrices. We transfer the original equations to a system of algebraic equations using operational matrices and collocation method. The convergence analysis of the presented method is discussed. Few examples are presented to show the efficiency of the presented method.