Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives. (November 2020)

• Record Type: Journal Article
• Authors: Dehestani, H.; Ordokhani, Y.; Razzaghi, M.
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Fractional Gegenbauer functions -- Atangana-Baleanu-Caputo variable-order fractional derivative -- Modified operational matrix of integration -- Error analysis; 34A08 -- 26A33 -- 65L60; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110111
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Fractional differential equations with the ABC-VO fractional derivative are solved. New functions called fractional Gegenbauer functions are defined. We acquired the modified-operational matrix of the integration with zero error. The method has an excellent performance in the proposed. This method is well done even if a small number of these functions are used. Abstract: The main idea of this paper is to establish the novel fractional Gegenbauer functions (FGFs) for solving three kinds of fractional differential equations generated by the variable-order fractional derivatives in the Atangana-Baleanu-Caputo (ABC) sense. The numerical scheme is discussed based on the modified operational matrices (MOMs) of Atangana-Baleanu variable-order (AB-VO) fractional integration and the delay operational matrix. The methodology of obtaining the MOMs of integration is calculated with high accuracy. So that the precision of the computation method is influenced directly by the proposed matrix. In addition, we investigate the error analysis of the proposed approach. At last, several numerical experiments are employed to clarify the performance and efficiency of the method.