The conformable fractional grey system model

TL;DR

This paper introduces a new conformable fractional grey system model that simplifies fractional order calculations, improving prediction accuracy and efficiency in natural gas production forecasting.

Contribution

The paper proposes a novel conformable fractional accumulation and difference, leading to a simpler and more effective grey model for time series prediction.

Findings

CFGM outperforms existing FGM models in 165 subcases

Numerical example demonstrates the model's feasibility and simplicity

Real-world case studies confirm improved forecasting accuracy

Abstract

The fractional order grey models (FGM) have appealed considerable interest of research in recent years due to its higher effectiveness and flexibility than the conventional grey models and other prediction models. However, the definitions of the fractional order accumulation (FOA) and difference (FOD) is computationally complex, which leads to difficulties for the theoretical analysis and applications. In this paper, the new definition of the FOA are proposed based on the definitions of Conformable Fractional Derivative, which is called the Conformable Fractional Accumulation (CFA), along with its inverse operation, the Conformable Fractional Difference (CFD). Then the new Conformable Fractional Grey Model (CFGM) based on CFA and CFD is introduced with detailed modelling procedures. The feasibility and simplicity and the CFGM are shown in the numerical example. And the at last the comprehensive real-world case studies of natural gas production forecasting in 11 countries are presented, and results show that the CFGM is much more effective than the existing FGM model in the 165 subcases.