Arabian Journal of Mathematics

, Volume 7, Issue 2, pp 147–158 | Cite as

Non-differentiability and fractional differentiability on timescales

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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.

Mathematics Subject Classification

26E70 26A33 28A80 

Notes

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Mehdi Nategh
    • 1
    • 2
  • Abdolali Neamaty
    • 2
  • Bahram Agheli
    • 3
  1. 1.Department of Mathematics and StatisticsMissouri S & TRollaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of MazandaranBabolsarIran
  3. 3.Department of Mathematics, Qaemshahr BranchIslamic Azad UniversityQaemshahrIran

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