Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Fractional Derivatives of Differentiable Functions are
  Integer-order Derivatives or Zero   In this paper we prove that local fractional derivatives of differentiable
functions are integer-order derivative or zero operator. We demonstrate that
the local fractional derivatives are limits of the left-sided Caputo fractional
derivatives. The Caputo derivative of fractional order alpha of function f(x)
is defined as a fractional integration of order (n-alpha) of the derivative
f^(n)(x) of integer order n. The requirement of the existence of integer-order
derivatives allows us to conclude that the local fractional derivative cannot
be considered as the best method to describe nowhere differentiable functions
and fractal objects. We also prove that unviolated Leibniz rule cannot hold for
derivatives of orders alpha, which are not equal to one.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th