A time power-based grey model with conformable fractional derivative and its applications. (February 2022)

• Record Type: Journal Article
• Authors: Wu, Wen-Ze; Zeng, Liang; Liu, Chong; Xie, Wanli; Goh, Mark
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Conformable fractional derivative -- Grey modeling technique -- Time power -- Particle swarm optimization; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111657
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: A time power-based grey model with conformable fractional derivative is proposed. The particle swarm optimization (PSO) technique is employed to determine the optimal emerging coefficients for the newly-designed model. Four cases are used to certify the superiority of the newly-designed model in contrast with other benchmarks. Abstract: The fractional grey model and its deformation forms have been appealed interest of research in practice due to its strong adaptability by merits of falling from the integer-order form into the fractional. This paper proposes an optimised time power-based grey model by the introduction of conformable fractional derivative into the conventional model. As a result, a newly-designed approach, namely the time power-based grey model with conformable fractional derivative (referred to as CFGM( ϕ, 1, t α )), is proposed thereby. Specifically, the model establishment, system parameter estimation and explicit expression are comprehensively implemented. In particular, several properties for the proposed approach are emphasized to interpret the superiority of the newly-designed model from a theoretical analysis perspective. The particle swarm optimization technique is then employed to determine the emerging coefficients such as the order of the conformable fractional derivative and time-power coefficient. Finally, four real-world cases are chosen to certify the applicability of the proposed model in contrast with other benchmark models and, the empirical results show that the newly-designed model outperforms other competing models, thus obtaining some managerial insights from these numerical experiments.