These examples come from Fractional-Order Nonlinear Systems, and can serve as companions to reproduce these well known fractional order chaotic systems in Julia.

FractionalDiffEq.jl also has impressive capability for solving Nonlinear system of FODEs:

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Fractional Order Arneodo System

Fractional Order Arneodo System

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Fractional Order Brusselator System

Fractional Order Brusselator System

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Fractional Order Chen System

Fractional orderChen system:

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Fractional Order Duffing System

Fractional Order Duffing System

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An example of system of Fractional Difference Equations

An example of system of Fractional Difference Equations

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Fractional Order Genesio-Tesi System

Fractional Order Genesio-Tesi System

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Fractional Order Hadley System

Fractional Order Hadley System

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Fractional Order Labyrinth System

Fractional Order Labyrinth System

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Fractional Order Liu System

Fractional Order Liu System

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Fractional Order Lotka Volterra System

Fractional Order Lotka Volterra System

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Fractional Order Lu System

Fractional Order Lu System

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Fractional Order Qi System

Since the Qi chaotic system is depicted as:

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Fractional Order Rossler System

Fractional Order Rossler System

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Fractional Order Van der Pol Oscillator

Fractional Order Van der Pol Oscillator