Grey Time Power Model with Caputo Fractional Derivative

Abstract

In this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-tangent-function transformation is used to improve the smoothness of the data sequence, and a grey time power model is obtained, which has higher accuracy than the sinusoidal-function transformation, negative-exponential-function transformation and logarithmic-function transformation. The form and application range of the model are generalized.

Keywords

• grey time power model
• Caputo fractional derivative
• Laplace transform
• linear-tangent-function transformation
• smooth ratio