Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-Fractional KdV Equation: Formulation and Solution using Variational
  Methods   In this work, the semi-inverse method has been used to derive the Lagrangian
of the Korteweg-de Vries (KdV) equation. Then, the time operator of the
Lagrangian of the KdV equation has been transformed into fractional domain in
terms of the left-Riemann-Liouville fractional differential operator. The
variational of the functional of this Lagrangian leads neatly to Euler-Lagrange
equation. Via Agrawal's method, one can easily derive the time-fractional KdV
equation from this Euler-Lagrange equation. Remarkably, the time-fractional
term in the resulting KdV equation is obtained in Riesz fractional derivative
in a direct manner. As a second step, the derived time-fractional KdV equation
is solved using He's variational-iteration method. The calculations are carried
out using initial condition depends on the nonlinear and dispersion
coefficients of the KdV equation. We remark that more pronounced effects and
deeper insight into the formation and properties of the resulting solitary wave
by additionally considering the fractional order derivative beside the
nonlinearity and dispersion terms.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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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: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex