Benaoumeur BAYOUR, Delfim F. M. TORRES

Structural derivatives on time scales

We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some self-similar functions. Some properties of the new operator are proved and illustrated with examples.

Keywords:

Hausdorff derivative of a function with respect to a fractal measure, structural and fractal derivatives, self-similarity time scales, hilger derivative of non-integer order,

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