Non-differentiability and fractional differentiability on timescales

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 illustr...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 2; pp. 147 - 158
Main Authors Nategh, Mehdi, Neamaty, Abdolali, Agheli, Bahram
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Subjects
Derivatives (Mathematics)
Difference equations
Mathematical research
Mathematics
Mathematics and Statistics
Mean value theorems (Calculus)
Self-similarity
Theorems
26E70
28A80
26A33
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-017-0185-1