Generalized Hukuhara diamond-alpha derivative of fuzzy valued functions on time scales

Abstract

In the literature, the delta and nabla derivatives have been considered separately in the study of fuzzy number valued functions on time scales. In this paper, to unify these two derivatives for fuzzy number valued functions, we propose a new dynamic derivative called the diamond-alpha derivative, defined via the generalized Hukuhara difference. We establish several fundamental properties of the diamond-alpha derivative and investigate a particular class of fuzzy initial value problems on time scales with respect to this new derivative. Additionally, we provide numerical examples to illustrate our results.

Keywords

• Time scale
• diamond-alpha derivative
• generalized Hukuhara difference
• fuzzy differential equations

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