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Table 6 The maximum absolute errors \(E_{x}\) and \(E_{u}\) at \(\mathcal{N} = 3\) 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 1.0231e − 3 1.9131e − 2 4.0523e − 5
0.5 2.4753e − 3 4.4331e − 2 2.0670e − 4
0.8 3.8530e − 3 6.4411e − 2 4.1156e − 4
1 4.6373e − 3 7.4699e − 2 5.3097e − 4
1.2 5.2771e − 3 8.2464e − 2 6.2030e − 4
1.5 5.9209e − 3 8.9499e − 2 6.8711e − 4
α = 0.9 0.2 2.3858e − 3 3.8860e − 2 1.5799e − 4
0.5 5.5632e − 3 8.1363e − 2 6.7525e − 4
0.8 7.7283e − 3 1.0371e − 1 1.0608e − 3
1 8.5173e − 3 1.0894e − 1 1.1381e − 3
1.2 5.4391e − 3 1.6713e − 1 3.2128e − 3
1.5 6.0557e − 3 1.6509e − 1 2.8066e − 3