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Psi-Series Solution of Fractional Ginzburg-Landau Equation
One-dimensional Ginzburg-Landau equations with derivatives of noninteger
order are considered. Using psi-series with fractional powers, the solution of
the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order
behaviours of solutions about an arbitrary singularity, as well as their
resonance structures, have been obtained. It was proved that fractional
equations of order with polynomial nonlinearity of order have the
noninteger power-like behavior of order near the singularity.Comment: LaTeX, 19 pages, 2 figure
Diffusion on middle- Cantor sets
In this paper, we study -calculus on generalized Cantor sets,
which have self-similar properties and fractional dimensions that exceed their
topological dimensions. Functions with fractal support are not differentiable
or integrable in terms of standard calculus, so we must involve local
fractional derivatives. We have generalized the -calculus on the
generalized Cantor sets known as middle- Cantor sets. We have suggested a
calculus on the middle- Cantor sets for different values of with
. Differential equations on the middle- Cantor sets have been
solved, and we have presented the results using illustrative examples. The
conditions for super-, normal, and sub-diffusion on fractal sets are given.Comment: 15 pages, 11 figure
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