A time power-based grey model with conformable fractional derivative and its applications

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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,tα)), 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.