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Theory and Modern Applications

Table 1 Numerical results of Example 5.1 when \(n=30\)

From: An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

t

α = 0.95

α = 0.9

α = 0.85

RKM

Res(t)

RKM

Res(t)

RKM

Res(t)

0.1

0.0095

3.495 × 10−6

0.0087

3.015 × 10−4

0.0120

4.102 × 10−4

0.2

0.0269

3.441 × 10−6

0.0281

8.575 × 10−4

0.0351

1.036 × 10−3

0.3

0.0502

4.195 × 10−6

0.0525

1.322 × 10−3

0.0615

1.448 × 10−3

0.4

0.0770

4.542 × 10−6

0.0797

1.525 × 10−3

0.0890

1.526 × 10−3

0.5

0.1053

4.282 × 10−6

0.1073

1.380 × 10−3

0.1155

1.245 × 10−3

0.6

0.1330

3.282 × 10−6

0.1336

8.837 × 10−4

0.1399

6.530 × 10−4

0.7

0.1586

1.548 × 10−6

0.1573

9.206 × 10−5

0.1611

1.653 × 10−4

0.8

0.1810

7.694 × 10−7

0.1775

8.970 × 10−4

0.1786

1.108 × 10−3

0.9

0.1994

3.720 × 10−6

0.1937

1.970 × 10−3

0.1923

2.077 × 10−3

1.0

0.2134

6.824 × 10−6

0.2058

2.675 × 10−3

0.2022

2.679 × 10−3