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An exploration of combined dynamic derivatives on time scales and their applications. (English) Zbl 1114.26004
The purpose of the paper is to explore basic properties of the first and second order $\diamond_\alpha$ derivatives which are linear combinations of $\Delta$ and $\nabla$ dynamic derivatives on time scales. Definitions of the $\diamond_\alpha$ derivatives are introduced and basic properties of the combined dynamic derivatives, as well as differences between the combined and standard dynamic derivatives are investigated. Proper differentiation rules for the $\diamond_\alpha$ derivatives are established. The change of variable formulae for the corresponding integrals are shown. The authors also present a number of computational experiments with the combined derivatives and integrals.

26A24Differentiation of functions of one real variable
Full Text: DOI
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