Fractional Order Hadley System

\[\begin{cases} {_{t_0}^{ABC}D_t^\alpha}x(t)=-y^2-z^2-ax+a\zeta\\ {_{t_0}^{ABC}D_t^\alpha}y(t)=xy-bxz-y+\delta\\ {_{t_0}^{ABC}D_t^\alpha}z(t)=bxy+xz-z\\ \end{cases}\]

using FractionalDiffEq, Plots

t0=0;tfinal=50;h=0.01
α = [0.99, 0.99, 0.99]
u0 = [-0.1; 0.1; -0.1]
function fun(du, u, p, t)
    a=0.2;b=4;ζ=8;δ=1;
    du[1] = -u[2]^2-u[3]^2-a*u[1]+a*ζ
    du[2] = u[1]*u[2]-b*u[1]*u[3]-u[2]+δ
    du[3] = b*u[1]*u[2]+u[1]*u[3]-u[3]
end
prob = FODESystem(fun, α, u0, (t0, tfinal))
sol = solve(prob, h, AtanganaSedaAB())

plot(sol, vars=(1,2,3) title="Fractional Order Hadley System")

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