A computational method based on the generalized Lucas polynomials for fractional optimal control problems

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Approximate solutions of \(\mathfrak{V}(\tau )\) for various values of α where \(N=8 \) along with CPU time in Example 1

τ	α = 0.5	α = 0.6	α = 0.7	α = 0.8	α = 0.9	α = 0.95	α = 1	Exact
0.1	0.62584500	0.68666710	0.74323669	0.79325450	0.83580800	0.85428224	0.87097241	0.87097241
0.2	0.56228260	0.59399381	0.63261220	0.67495369	0.71800733	0.73902711	0.75939333	0.75939333
0.3	0.48110286	0.51388507	0.54780242	0.58422853	0.62300270	0.64294652	0.66302744	0.66302744
0.4	0.44034576	0.46174082	0.48597000	0.51372055	0.54520062	0.56221791	0.57994422	0.57994422
0.5	0.42948855	0.43256175	0.44289130	0.45937629	0.48142481	0.49436936	0.50847923	0.50847923
0.6	0.40206008	0.40260088	0.40655351	0.41495118	0.42841422	0.43714154	0.44720078	0.44720078
0.7	0.36920422	0.37274202	0.37468952	0.37781684	0.38410943	0.38887743	0.39488126	0.39488126
0.8	0.36867554	0.35967523	0.35322486	0.34904107	0.34778268	0.34856867	0.35047254	0.35047254
0.9	0.36471034	0.35082831	0.33811766	0.32708465	0.31841614	0.31526500	0.31308497	0.31308496
1.0	0.37517682	0.34890244	0.32857936	0.31083431	0.29508251	0.28813145	0.28196953	0.28196953
CPU time	0.625 s	0.610 s	0.609 s	0.578 s	0.547 s	0.594 s	0.515 s	–