Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Leibniz integral rules for Riemann-Liouville and Caputo
  fractional derivatives and their applications   In recent years, the theory for Leibniz integral rule in the fractional sense
has not been able to get substantial development. As an urgent problem to be
solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type
differentiation operators with general fractional-order of $n-1 <\alpha \leq
n$, $n \in \mathbb{N}$ . A rule of fractional differentiation under integral
sign with general order is necessary and applicable tool for verification by
substitution for candidate solutions of inhomogeneous multi-term fractional
differential equations. We derive explicit analytical solutions of generalized
Bagley-Torvik equations in terms of recently defined bivariate Mittag-Leffler
type functions that based on fractional Green's function method and verified
solutions by substitution in accordance by applying the fractional Leibniz
integral rule. Furthermore, we study an oscillator equation as a special case
of differential equations with multi-orders via the Leibniz integral rule.

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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
30
The categories of this paper are: q-alg