We assume that initial conditions of the SO-DCTS algorithm are, where is initial time offset for node.
If β and γ are independent of τ 0, then the solution y t, τ 0, y 0) of the initial value problems of fractional order differential equation with Caputo's derivative of (2.2.3) is initial time difference uniformly equi-bounded with respect to the solution x(t - η, t 0, x 0).
If T and γ are independent of τ 0, then the solution y t, τ 0, y 0) of the initial value problems of fractional order differential equation with Caputo's derivative of (2.2.3) is initial time difference uniformly quasi-equi-asymptotically stable with respect to the solution x(t - η, t 0, x 0).
Then, if fractional order comparison system (3.1.2) is uniformly quasi-equi-asymptotically stable, the solution y t, τ 0, y 0) of (2.2.3) through (τ 0, y 0) is initial time difference uniformly quasi-equi-asymptotically stable for t ≥ τ 0 ∈ ℝ+ with respect to the solution x(t - η, t 0, x 0) through (t 0, x 0) where x t, t 0, x 0) is the solution of (2.2.1) through (t 0, x 0).
Then, if fractional order comparison system (3.1.2) is uniformly bounded, the solution y t, τ 0, y 0) of (2.2.3) through (τ 0, y 0) is initial time difference uniformly bounded for t ≥ τ 0 ∈ ℝ+ with respect to the solution x(t - η, t 0, x 0) through (t 0, x 0) where x t, t 0, x 0) is the solution of (2.2.1) through (t 0, x 0).
Hence, if all the hypotheses of the Theorem 3.2.3 for q = 1 have been satisfied, then the solution y t, τ 0, y 0) of (4.4) is initial time difference Lagrange stable with respect to the solution x ̃ ( t, τ 0, x 0 ) of (4.3) for t ≥ τ 0, τ 0 ∈ ℝ since we have D * + V ( t, y - x ̃ ) ≤ - 2 V ( t, y - x ̃ ).
In subjects, AUC0 96h values in pleural fluid and plasma were 17831 ± 6439 μgh/mL and 778 ± 328 μgh/mL, respectively, and Tmax values were initial time and 6.67 h after administration and the corresponding Cmax values were 558 ± 44 μg/mL and 12.89 ± 6.86 μg/mL, respectively.
The responses studied are initial setting time, final setting time, and CCS after 4, 8, and 24 h curing.
t n is a time state such that tn + 1 − t n = Δt and n = T/∆t is the final time horizon, but n = 0 is the initial time state being solved for.
From the in vivo levels of endogenous MT in different populations (Fig. 3), the secretion time of 18 00 was selected to be the initial time to administer MT (0 h).
Furthermore, there is an initial time delay from the time of diagnosis of 4 6 weeks before a new steady-state A1C can be achieved (8).
