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Table 1 The absolute error for Example 7.1 for different estimations of \(k, M\) at \(\alpha=1\)

From: Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method

x k = 3,M = 4 k = 4,M = 5 k = 5,M = 6 k = 6,M = 7 k = 7,M = 8
0.1 1.6403 × 10−7 1.4281 × 10−9 2.0695 × 10−10 1.574 × 10−12 4.2461 × 10−14
0.2 2.5018 × 10−7 2.7054 × 10−9 4.1957 × 10−10 2.1255 × 10−12 5.0451 × 10−14
0.3 1.4102 × 10−7 4.7082 × 10−9 1.4795 × 10−10 2.1443 × 10−12 2.6821 × 10−14
0.4 2.1512 × 10−7 6.5014 × 10−9 3.1759 × 10−10 3.1682 × 10−12 3.5171 × 10−14
0.5 1.9018 × 10−7 2.7802 × 10−9 5.6087 × 10−10 4.6833 × 10−12 2.6417 × 10−14
0.6 4.4186 × 10−7 2.3081 × 10−9 2.2781 × 10−10 3.6951 × 10−12 1.7129 × 10−13
0.7 3.1042 × 10−6 4.2721 × 10−8 1.7309 × 10−9 1.2071 × 10−11 2.6357 × 10−13
0.8 4.3051 × 10−6 1.3062 × 10−8 2.9053 × 10−9 2.2721 × 10−11 3.6457 × 10−13
0.9 3.2101 × 10−6 2.3775 × 10−8 2.0941 × 10−9 3.2974 × 10−11 1.6864 × 10−13