Fractional Ginzburg–Landau equation for fractal media

By Vasily E. Tarasov, George Zaslavsky. 2005

214 citations recorded by the source corpus.

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equation or nonlinear Schrodinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c6ee956e1e063017956ffbbe02835ad44882d713

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Citations in the corpus

A Central Difference Numerical Scheme for Fractional Optimal Control Problems (2008, methodology): “Tarasov and Zaslavsky have used the variational Euler–Lagrange equation to derive fractional generalization of the Ginzburg–Landau equation for fractal media (Tarasov and Zaslavsky, 2005) and dynamic systems subjected to non-holonomic constraints (Tarasov and Zaslavsky, 2006).”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, methodology): “The fractional Euler–Lagrange equation has recently been presented in the literature (Almeida and Torres, 2009; Atanacković et al., 2007; Bastos et al., 2011; Frederico and Torres, 2007; Malinowska and Torres, 2010; Muslih and Baleanu, 2005; Stanislavsky, 2006; Tarasov and Zaslavsky, 2005, 2006).”
Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative (2007, methodology): “Tarasov and Zaslavsky (2005) used the variational Euler– Lagrange equation to derive fractional generalization of the Ginzburg–Landau equation for fractal media.”
A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems (2007, methodology): “Tarasov and Zaslavsky (2005) have used the variational Euler–Lagrange equation to derive fractional generalization of the Ginzburg–Landau equation for fractal media.”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[177] V.”
Fractional optimal control problems: a pseudo-state-space approach (2011, methodology): “Tarasov and Zaslavsky (2005) have used the variational EulerLagrange equation to derive fractional generalization of the Ginzburg-Landau equation for fractal media.”
Fractional Vector Calculus and Fractional Maxwell's Equations (2008, background): “These operations are connected with fractional derivatives only by Fourier transforms (see [28]).”
The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Such models have attracted the attention of community in recent years [8, 239, 327, 405, 408].”