Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality for the left and right fractional derivatives   We prove duality between the left and right fractional derivatives,
independently on the type of fractional operator. Main result asserts that the
right derivative of a function is the dual of the left derivative of the dual
function or, equivalently, the left derivative of a function is the dual of the
right derivative of the dual function. Such duality between left and right
fractional operators is useful to obtain results for the left operators from
analogous results on the right operators and vice versa. We illustrate the
usefulness of our duality theory by proving a fractional integration by parts
formula for the right Caputo derivative and by proving a Tonelli-type theorem
that ensures the existence of minimizer for fractional variational problems
with right fractional operators.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: econ