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Table 2 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 1 ρ \(E_{x}\) \(E_{u}\) \(\mathcal{J}\)
α = 0.5 0.2 1.1055e − 3 2.6344e − 2 4.6858e − 6
0.5 1.9918e − 3 4.4570e − 2 1.7460e − 5
0.8 2.1700e − 3 4.6071e − 2 2.3426e − 5
1 2.0169e − 3 4.1521e − 2 2.1739e − 5
1.2 1.7212e − 3 3.4446e − 2 1.6844e − 5
1.5 1.1225e − 3 2.1604e − 2 7.6890e − 6
α = 0.9 0.2 1.9345e − 3 4.1959e − 2 1.6842e − 5
0.5 2.4209e − 3 4.8170e − 2 3.5887e − 5
0.8 1.4101e − 3 2.6196e − 2 1.6130e − 5
1 4.9785e − 4 8.8228e − 3 2.3605e − 6
1.2 8.1160e − 4 1.0918e − 2 1.9380e − 6
1.5 2.6130e − 3 4.4556e − 2 3.9022e − 5