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Table 7 The maximum absolute errors \(E_{x}\) and \(E_{u}\) at \(\mathcal{N} = 5\) 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 1.6865e − 5 1.1069e − 3 5.8648e − 8
0.5 2.7834e − 5 1.8933e − 3 1.6285e − 7
0.8 3.0404e − 5 1.9449e − 3 1.6076e − 7
1 2.9145e − 5 1.7279e − 3 1.2039e − 7
1.2 2.5093e − 5 1.3995e − 3 7.4509e − 8
1.5 1.5777e − 5 8.2731e − 4 2.3702e − 8
α = 0.9 0.2 3.2317e − 5 1.9834e − 3 1.6158e − 7
0.5 4.5113e − 5 2.2291e − 3 1.9362e − 7
0.8 2.7368e − 5 1.1331e − 3 4.6760e − 8
1 9.3964e − 6 3.5368e − 4 4.3214e − 9
1.2 5.2136e − 6 3.1529e − 4 4.6852e − 9
1.5 1.4204e − 5 9.2895e − 4 3.5294e − 8