Page 192 - Mathematical Techniques of Fractional Order Systems

180 Mathematical Techniques of Fractional Order Systems

(A) Case with α = 0.5
6
Noncoupled
||φ 1 (t)|| 4 Coupled

2
0 500 1000 1500
Case with α = 0.7
10
Noncoupled
||φ 1 (t)|| 5 Coupled
0
0 500 1000 1500
Case with α = 0.9
10
Noncoupled
||φ 1 (t)|| 5 Coupled
0
0 500 1000 1500
Case with α = 1
10
Noncoupled
||φ 1 (t)|| 5 Coupled
0
0 500 1000 1500
Time (s)
(B) Case with α = 0.5
6
Noncoupled
4
||φ 2 (t)|| 2 Coupled
0
0 500 1000 1500
Case with α = 0.7
6
Noncoupled
||φ 2 (t)|| 2 Coupled
4
0
0 500 1000 1500
Case with α = 0.9
6
Noncoupled
4
||φ 2 (t)|| 2 Coupled
0
0 500 1000 1500
Case with α = 1
6
Noncoupled
||φ 2 (t)|| 4 2 Coupled
0
0 500 1000 1500
Time (s)
FIGURE 6.4 Evolution for different values of α, using NCFOAL & CFOAL of the (A)
Oφ 1 tðÞO, and (B) Oφ 2 tðÞO. Noisy environment.