Chaotic dynamics of the fractional Lorenz system.

By I. Grigorenko, E. Grigorenko. Physical Review Letters, 2003

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New results on stability and stabilization of a class of nonlinear fractional-order systems (2013, positive): “Fractional-order Lorenz system[31] can be described by ⎧⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ dx1 dtα = a(x2 − x1), dx2 dtα = bx1 − x1x3 − x2, dx3 dtα = x1x2 − cx3, (37)”
Chaos in the Newton–Leipnik system with fractional order (2008, background): “Moreover, in the last decade many researchers have found that chaotic attractors indeed exist in fractional-order systems [15–20].”
Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform (2013, background): “Based on experimental data fractional partial differential equations for seepage flow in porous media are suggested in [5], and differential equations with fractional order have recently proved to be valuable tools to the modeling of many physical phenomena [6].”
Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, background): “On the basis of experimental data, fractional partial differential equations for seepage flow in porous media are suggested in [5], and differential equations with fractional order have recently proved to be valuable tools to the modeling of many physical phenomena [1, 6].”