Abstract
This work deals with concepts of non-differentiability and a non-integer order differential on timescales. Through an investigation of a local non-integer order derivative on timescales, a mean value theorem (a fractional analog of the mean value theorem on timescales) is presented. Then, by illustrating a vanishing property of this derivative, its objectivity is discussed. As a first-hand result, the potentials and capability of this fractional derivative connected to nonsmooth analysis, including non-differentiable paths and a class of self-similar fractals, are stated. It is stated that the non-integer order derivative never vanishes almost everywhere. It has been shown that with the help of changing the order of differentiability on a q-timescale, the non-differentiability disappears.
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Nategh, M., Neamaty, A. & Agheli, B. Non-differentiability and fractional differentiability on timescales. Arab. J. Math. 7, 147–158 (2018). https://doi.org/10.1007/s40065-017-0185-1
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DOI: https://doi.org/10.1007/s40065-017-0185-1