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Table 4 The maximum absolute errors \(E_{x}\) and \(E_{u}\) at \(\mathcal{N} = 7\) and various values of α, ρ for \(x(t)\) and \(u(t)\), respectively

From: Numerical solutions of fractional optimal control with Caputo–Katugampola derivative

Example 1 ρ \(E_{x}\) \(E_{u}\) \(\mathcal{J}\)
α = 0.5 0.2 1.3164e − 5 4.5200e − 3 1.3367e − 9
0.5 1.8844e − 5 5.8255e − 3 2.8468e − 9
0.8 1.6082e − 5 4.5318e − 3 2.1206e − 9
1 1.2589e − 5 3.3533e − 3 1.3028e − 9
1.2 8.9696e − 6 2.2683e − 3 6.5501e − 10
1.5 4.3692e − 6 1.0322e − 3 1.4883e − 10
α = 0.9 0.2 1.7852e − 5 5.9378e − 3 2.7782e − 9
0.5 1.4755e − 5 4.1134e − 3 2.0502e − 9
0.8 5.2965e − 6 1.2964e − 3 2.9148e − 10
1 1.2791e − 6 2.9425e − 4 1.8509e − 11
1.2 1.3873e − 5 2.7262e − 4 6.4287e − 12
1.5 1.4947e − 5 4.8645e − 4 5.0808e − 11