Structural derivatives on time scales

Abstract

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.

This is a preprint of a paper whose final and definite form is with 'Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.', ISSN: 1303-5991. Submitted 14 May 2018; Article revised 18 Nov 2018; Article accepted for publication 23 Nov 2018