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Theory and Modern Applications

Table 1 The absolute errors for different α, m of the FEFs and \(M = 6\) of the Legendre wavelet

From: Fractional-order Euler functions for solving fractional integro-differential equations with weakly singular kernel

x

α = 1

α = 1/2

Legendre wavelet [38]

m = 4

m = 5

m = 6

m = 4

M = 6

0.1

6.06e − 4

4.55e − 5

2.18e − 5

1.63e − 16

5.55112e − 16

0.2

1.05e − 4

1.61e − 5

1.03e − 5

1.06e − 15

6.66134e − 16

0.3

2.62e − 5

3.15e − 5

1.59e − 5

1.04e − 15

9.15934e − 16

0.4

6.32e − 5

3.35e − 5

5.81e − 6

5.22e − 16

1.27676e − 15

0.5

9.66e − 5

3.10e − 6

1.76e − 5

1.42e − 16

1.63758e − 15

0.6

5.36e − 5

3.68e − 5

2.63e − 6

6.75e − 16

2.04003e − 15

0.7

4.01e − 5

2.80e − 5

1.82e − 5

8.59e − 16

2.52576e − 15

0.8

1.12e − 4

2.43e − 5

7.46e − 6

5.14e − 16

3.27516e − 15

0.9

4.48e − 5

4.63e − 5

2.57e − 5

5.06e − 16

3.77476e − 15