Table 3 Comparison between errors of q-HAShTM, FNDM and q-HATM with GIRPSM for example 2 at \(\alpha = 1\), \(\rho = 0.001\).

From: Analytical treatment of the fractional Zakharov–Kuznetsov equation via the generalized integral residual power series method

x = y

t

Numerical solution

GIRPSM

q-HATM34

FNDM34

q-HAShTM36

0.02

2*\({10}^{-2}\)

4.9926*\({10}^{-9}\)

4.9926*\({10}^{-9}\)

4.9926*\({10}^{-9}\)

4.9926*\({10}^{-9}\)

4*\({10}^{-2}\)

9.9852*\({10}^{-9}\)

9.9852*\({10}^{-9}\)

9.9852*\({10}^{-9}\)

9.9852*\({10}^{-9}\)

6*\({10}^{-2}\)

1.4977*\({10}^{-8}\)

1.4979*\({10}^{-8}\)

1.4979*\({10}^{-8}\)

1.4977*\({10}^{-8}\)

8*\({10}^{-2}\)

1.9970*\({10}^{-8}\)

1.9970*\({10}^{-8}\)

1.9970*\({10}^{-8}\)

1.9970*\({10}^{-8}\)

1*\({10}^{-1}\)

2.4963*\({10}^{-8}\)

2.4963*\({10}^{-8}\)

2.4963*\({10}^{-8}\)

2.4963*\({10}^{-8}\)

0.06

2*\({10}^{-2}\)

4.9934*\({10}^{-9}\)

4.9963*\({10}^{-9}\)

4.9963*\({10}^{-9}\)

4.9934*\({10}^{-9}\)

4*\({10}^{-2}\)

9.9869*\({10}^{-9}\)

9.9869*\({10}^{-9}\)

9.9869*\({10}^{-9}\)

9.9869*\({10}^{-9}\)

6*\({10}^{-2}\)

1.4980*\({10}^{-8}\)

1.4980*\({10}^{-8}\)

1.4980*\({10}^{-8}\)

1.4980*\({10}^{-8}\)

8*\({10}^{-2}\)

1.9973*\({10}^{-8}\)

1.9974*\({10}^{-8}\)

1.9974*\({10}^{-8}\)

1.9973*\({10}^{-8}\)

1*\({10}^{-1}\)

2.4967*\({10}^{-8}\)

2.4967*\({10}^{-8}\)

2.4967*\({10}^{-8}\)

2.4967*\({10}^{-8}\)

0.1

2*\({10}^{-2}\)

4.9951*\({10}^{-9}\)

4.9952*\({10}^{-9}\)

4.9952*\({10}^{-9}\)

4.9951*\({10}^{-9}\)

4*\({10}^{-2}\)

9.9903*\({10}^{-9}\)

9.9904*\({10}^{-9}\)

9.9904*\({10}^{-9}\)

9.9904*\({10}^{-9}\)

6*\({10}^{-2}\)

1.4985*\({10}^{-8}\)

1.4986*\({10}^{-8}\)

1.4986*\({10}^{-8}\)

1.4985*\({10}^{-8}\)

8*\({10}^{-2}\)

1.9980*\({10}^{-8}\)

1.9981*\({10}^{-8}\)

1.9981*\({10}^{-8}\)

1.9980*\({10}^{-8}\)

1*\({10}^{-1}\)

2.4975*\({10}^{-8}\)

2.4976*\({10}^{-8}\)

2.4976*\({10}^{-8}\)

2.4976*\({10}^{-8}\)

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