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Table 3 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 1 ρ \(E_{x}\) \(E_{u}\) \(\mathcal{J}\)
α = 0.5 0.2 1.3154e − 4 9.1543e − 3 3.6957e − 8
0.5 2.0416e − 4 1.3077e − 2 9.6857e − 8
0.8 1.9006e − 4 1.1307e − 2 8.9359e − 8
1 1.5831e − 4 8.9932e − 3 6.3605e − 8
1.2 1.2060e − 4 6.5490e − 3 3.7228e − 8
1.5 6.5823e − 5 3.3397e − 3 1.0760e − 8
α = 0.9 0.2 2.1582e − 4 1.2958e − 2 9.2709e − 8
0.5 2.0571e − 4 1.0850e − 2 1.0133e − 7
0.8 8.7454e − 5 4.1592e − 3 2.1681e − 8
1 2.4125e − 5 1.0802e − 3 1.8261e − 9
1.2 6.6853e − 5 1.1549e − 3 8.3696e − 10
1.5 1.0467e − 4 2.8705e − 3 7.8248e − 9