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Theory and Modern Applications

Table 2 Comparison of LTVIM, HPM [17], HPTM [18], RPSM and HATM [20] on Example 4.2. Here \(\alpha = 1\) is used for all methods

From: A numerical method using Laplace-like transform and variational theory for solving time-fractional nonlinear partial differential equations with proportional delay

x

t

Absolute error

LTVIM

HPM [17], HPTM [18], RPSM and HATM [20]

0.25

0.25

1.38496 × 10−8

5.30400 × 10−7

0.50

8.79440 × 10−7

1.77350 × 10−5

0.75

9.89609 × 10−6

1.40870 × 10−4

1

5.46480 × 10−5

5.55306 × 10−4

0.50

0.25

5.53984 × 10−8

2.12200 × 10−6

0.50

3.51776 × 10−6

7.09430 × 10−5

0.75

3.95844 × 10−5

5.63482 × 10−4

1

2.18592 × 10−4

2.48712 × 10−3

0.75

0.25

1.24646 × 10−7

4.77400 × 10−6

0.50

7.91497 × 10−6

1.59621 × 10−4

0.75

8.90649 × 10−5

1.26783 × 10−3

1

4.91832 × 10−4

5.59603 × 10−3