Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator Ordering and Solution of Pseudo-Evolutionary Equations   The solution of pseudo initial value differential equations, either ordinary
or partial (including those of fractional nature), requires the development of
adequate analytical methods, complementing those well established in the
ordinary differential equation setting. A combination of techniques, involving
procedures of umbral and of operational nature, has been demonstrated to be a
very promising tool in order to approach within a unifying context
non-canonical evolution problems. This article covers the extension of this
approach to the solution of pseudo-evolutionary equations. We will comment on
the explicit formulation of the necessary techniques, which are based on
certain time- and operator ordering tools. We will in particular demonstrate
how Volterra-Neumann expansions, Feynman-Dyson series and other popular tools
can be profitably extended to obtain solutions of fractional differential
equations. We apply the method to a number of examples, in which fractional
calculus and a certain umbral image calculus play a role of central importance.

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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: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat