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On the Fractional-Order Logistic Equation with Two Different Delays

The fractional-order logistic equation with the two different delays r1, r2 > 0, Dα x(t) = ρx(t − r1)[1−x(t −r2)], t > 0 and ρ > 0, with the initial data x(t) = x0, t ≤ 0 are considered. The existence of a unique uniformly stable solution is studied and the Adams-type predictor-corrector method is applied to obtain the numerical solution.