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Table 8 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 2 ρ \(E_{x}\) \(E_{u}\) \(\mathcal{J}\)
α = 0.5 0.2 1.6127e − 6 2.1652e − 4 1.2871e − 9
0.5 2.3090e − 6 3.2683e − 4 2.7911e − 9
0.8 1.9487e − 6 2.9596e − 4 2.1390e − 9
1 1.4956e − 6 2.4174e − 4 1.3476e − 9
1.2 1.0266e − 6 1.8003e − 4 6.9875e − 10
1.5 4.6305e − 7 9.3728e − 5 1.6861e − 10
α = 0.9 0.2 1.3134e − 6 3.6940e − 4 3.0913e − 9
0.5 1.2270e − 6 3.3083e − 4 2.3244e − 9
0.8 6.0882e − 7 1.3317e − 4 3.4361e − 10
1 2.0735e − 7 3.5322e − 5 2.2453e − 11
1.2 2.2995e − 7 2.4759e − 5 1.6117e − 11
1.5 4.5864e − 7 5.5041e − 5 6.7793e − 11