2005
DOI: 10.1016/j.physa.2005.02.047
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Fractional Ginzburg–Landau equation for fractal media

Abstract: We derive the fractional generalization of the Ginzburg-Landau equation from the

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Cited by 185 publications
(133 citation statements)
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“…As it was shown in [14,15], the FEA appears in the infrared limit when the wave number k → 0 and some other conditions that will be derived later. At the same time, in many applied problems equations with FD can appear as an intrinsic feature of the system (see examples in reviews [2,9]).…”
Section: Introductionmentioning
confidence: 83%
See 1 more Smart Citation
“…As it was shown in [14,15], the FEA appears in the infrared limit when the wave number k → 0 and some other conditions that will be derived later. At the same time, in many applied problems equations with FD can appear as an intrinsic feature of the system (see examples in reviews [2,9]).…”
Section: Introductionmentioning
confidence: 83%
“…Its formal realization can be perfomed using the so-called "transform operator" [14]. Different applications of the operator have already been used to derive fractional sine-Gordon and fractional Hilbert equation [13], to study synchronization of coupled oscillators [14], and for fractional Ginzburg-Landau equation [15].…”
Section: Introductionmentioning
confidence: 99%
“…The differential operations are defined with respect to fractional powers of coordinates. These operations are connected with fractional derivatives only by Fourier transforms (see [28]). As a result, an "ideal" fractional vector calculus is not suggested.…”
Section: Other Approaches To Fractional Vector Calculusmentioning
confidence: 99%
“…It has been shown that Lagrangians involving fractional time derivatives lead to equations of motion with non-conservative classical forces. Recently, several researchers have explored this area and given new insight into this problem [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. A fractional calculus with variations which deal with problems containing both the left-and right derivatives has been developed [40].…”
Section: Introductionmentioning
confidence: 99%