Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilfer-Katugampola fractional derivative   We propose a new fractional derivative, the Hilfer-Katugampola fractional
derivative. Motivated by the Hilfer derivative this formulation interpolates
the well-known fractional derivatives of Hilfer, Hilfer-Hadamard,
Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl,
generalized and Caputo-type. As an application, we consider a nonlinear
fractional differential equation with an initial condition using this new
formulation. We show that this equation is equivalent to a Volterra integral
equation and demonstrate the existence and uniqueness of solution to the
nonlinear initial value problem.

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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys