Continuous grey model with conformable fractional derivative

TL;DR

This paper introduces a simplified grey prediction model using conformable fractional derivatives, aiming to retain the benefits of continuous fractional calculus while improving computational efficiency and practical applicability.

Contribution

The paper proposes a new grey model based on conformable fractional derivatives, simplifying calculations compared to existing continuous fractional-order models.

Findings

Model demonstrates good prediction accuracy in practical cases

Simplified computation enhances real-world applicability

Validates effectiveness through case studies

Abstract

The existing fractional grey prediction models mainly use discrete fractional-order difference and accumulation, but in the actual modeling, continuous fractional-order calculus has been proved to have many excellent properties, such as hereditary. Now there are grey models established with continuous fractional-order calculus method, and they have achieved good results. However, the models are very complicated in the calculation and are not conducive to the actual application. In order to further simplify and improve the grey prediction models with continuous fractional-order derivative, we propose a simple and effective grey model based on conformable fractional derivatives in this paper, and two practical cases are used to demonstrate the validity of the proposed model.