Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives

H. Dehestani, Y. Ordokhani and M. Razzaghi

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

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.

Keywords: Fractional Gegenbauer functions; Atangana-Baleanu-Caputo variable-order fractional derivative; Modified operational matrix of integration; Error analysis (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305087

DOI: 10.1016/j.chaos.2020.110111

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