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Theory and Modern Applications

Table 7 Optimality value “\(\mathcal{J}\)”, MAE of the state function “\(\phi (x)\)” and the control function “\(v(x)\)” for Example 6 using \(S_{1}\) when \(\nu =0.49\)

From: Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

M

SU-pseudo-GM

[48]

\(\mathcal{J}(v)\)

ϕ(x)

v(x)

\(\mathcal{J}(v)\)

Value

Time

2

4.9816e-16

0.012

1.7155e-08

2.7391e-08

3

7.5675e-16

0.021

2.5321e-08

3.8533e-08

4

4.3574e-16

0.035

2.0878e-08

4.8836e-08

4.7693e-06

5

4.5959e-16

0.044

2.2785e-08

5.7676e-08

1.4724e-06

6

8.4043e-15

0.071

2.4193e-08

1.5770e-07

5.3783e-07

7

6.7510e-13

0.099

1.2375e-07

5.6828e-06

8

8.7378e-13

0.139

2.2888e-07

3.5761e-06

1.0610e-07

9

5.4106e-14

0.181

5.4007e-08

5.7890e-07

5.4430e-07