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Theory and Modern Applications

Table 4 MAEs of \(\pmb{x(t)}\) at \(\pmb{\nu=1.9}\) for Example 3

From: An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems

N

α  =  β  = 0

α  =  β  = 1

\(\boldsymbol{\alpha=\beta=\frac{1}{2}}\)

\(\boldsymbol{-\alpha=\beta=\frac{1}{2}}\)

\(\boldsymbol{\alpha=-\beta=\frac{1}{2}}\)

2

9.18332⋅10−2

1.28493⋅10−1

1.12969⋅10−1

2.08594⋅10−1

1.86858⋅10−1

4

9.49903⋅10−5

1.06218⋅10−4

1.00982⋅10−4

8.21136⋅10−5

1.31015⋅10−4

6

7.49087⋅10−6

8.89075⋅10−6

8.17665⋅10−6

6.48240⋅10−6

1.13547⋅10−5

8

1.28702⋅10−6

1.57985⋅10−6

1.42115⋅10−6

1.13022⋅10−6

2.03692⋅10−6

10

3.29371⋅10−7

4.12868⋅10−7

3.65559⋅10−7

2.93441⋅10−7

5.32931⋅10−7

12

1.08092⋅10−7

1.37396⋅10−7

1.20205⋅10−7

9.74985⋅10−8

1.76861⋅10−7

14

4.20937⋅10−8

5.40342⋅10−8

4.68274⋅10−8

3.83620⋅10−8

6.92167⋅10−8

16

1.85795⋅10−8

2.40235⋅10−8

2.06582⋅10−8

1.70785⋅10−8

3.05888⋅10−8

18

9.02630⋅10−9

1.17344⋅10−8

1.00262⋅10−8

8.35794⋅10−9

1.48413⋅10−8

20

4.70400⋅10−9

6.12870⋅10−9

5.16233⋅10−9

4.30767⋅10−9

7.79998⋅10−9

22

3.35847⋅10−9

3.79853⋅10−9

4.10957⋅10−9

3.45753⋅10−9

3.86255⋅10−9