Local Fractional Fokker-Planck Equation
TLDR
Local fractional differential equations (LDFDE) as mentioned in this paper is a new class of differential equations, which involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time.Abstract:
We propose a new class of differential equations, which we call local fractional differential equations. They involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time. A local fractional analog of the Fokker-Planck equation has been derived starting from the Chapman-Kolmogorov condition. We solve the equation with a specific choice of the transition probability and show how subdiffusive behavior can arise.read more
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The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
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Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results
TL;DR: A modified Riemann-Liouville definition is proposed, which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one's.
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Chaotic dynamics of the fractional Lorenz system.
Ilia Grigorenko,Elena Grigorenko +1 more
TL;DR: A striking finding is that there is a critical value of the effective dimension Sigma(cr), under which the system undergoes a transition from chaotic dynamics to regular one.