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Theory and Modern Applications

Table 1 Absolute errors of \(\pmb{x(t)}\) at \(\pmb{\nu=1}\) , \(\pmb{\alpha=\beta=0}\) and various choices of N for Example 1

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

t

N  = 3

N  = 5

N  = 7

N  = 9

N  = 11

0.0

1.00212⋅10−3

5.05995⋅10−6

1.29671⋅10−8

2.01182⋅10−11

1.05293⋅10−12

0.1

5.07200⋅10−4

2.21852⋅10−6

1.20766⋅10−9

7.68471⋅10−12

2.41667⋅10−13

0.2

5.79556⋅10−4

1.73459⋅10−6

2.80427⋅10−9

7.20090⋅10−12

1.28452⋅10−13

0.3

8.89184⋅10−5

2.00164⋅10−6

5.29753⋅10−9

3.82827⋅10−12

1.27342⋅10−13

0.4

3.95506⋅10−4

8.36831⋅10−7

2.67200⋅10−10

3.21442⋅10−12

3.17301⋅10−13

0.5

5.70607⋅10−4

2.37092⋅10−6

5.25044⋅10−9

7.24365⋅10−12

2.22155⋅10−13

0.6

3.66024⋅10−4

6.99321⋅10−7

5.15504⋅10−10

3.46145⋅10−12

7.74935⋅10−14

0.7

8.45293⋅10−5

1.89552⋅10−6

4.89480⋅10−9

3.29469⋅10−12

2.95985⋅10−13

0.8

4.67865⋅10−4

1.36038⋅10−6

2.92884⋅10−9

6.64379⋅10−12

3.31734⋅10−13

0.9

3.12315⋅10−4

2.12016⋅10−6

5.80711⋅10−10

7.22222⋅10−12

3.55715⋅10−13