New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

Abstract

In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.

Keywords

• Discrete-time
• Fractional derivative
• Time scale
• bilinear transformation