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Theory and Modern Applications

Table 1 Numerical results of \(\Gamma _{q}(\sigma +1)\) and Δ for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.1 (Algorithm 1)

From: Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

n

\(q = \frac{ 1}{ 5}\)

\(q = \frac{ 1}{ 2}\)

\(q = \frac{7}{8}\)

\(\Gamma _{q}(\sigma +1)\)

Δ

\(\Gamma _{q}(\sigma +1)\)

Δ

\(\Gamma _{q}(\sigma +1)\)

Δ

1

1.3971

6.4927E + 00

2.6906

3.3713E + 00

4.1775

2.1713E − 01

2

1.3860

6.5444E + 00

2.4015

3.7771E + 00

2.5979

3.4916E − 01

3

1.3839

6.5547E + 00

2.2738

3.9892E + 00

1.8239

4.9733E − 01

4

1.3834

6.5568E + 00

2.2136

4.0976E + 00

1.3865

6.5422E − 01

5

1.3833

6.5572E + 00

2.1844

4.1524E + 00

1.1146

8.1380E − 01

6

1.3833

6.5573E + 00

2.1700

4.1800E + 00

9.3373

9.7145E − 01

7

1.3833

6.5573E + 00

2.1629

4.1938E + 00

8.0715

1.1238E + 00

8

1.3833

6.5573E + 00

2.1593

4.2007E + 00

7.1505

1.2685E + 00

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13

1.3833

6.5573E + 00

2.1559

4.2074E + 00

4.9118

1.8467E + 00

14

1.3833

6.5573E + 00

2.1558

4.2075E + 00

4.6925

1.9330E + 00

15

1.3833

6.5573E + 00

2.1558

4.2076E + 00

4.5115

2.0106E + 00

16

1.3833

6.5573E + 00

2.1558

4.2076E + 00

4.3610

2.0800E + 00

17

1.3833

6.5573E + 00

2.1558

4.2076E + 00

4.2349

2.1419E + 00

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75

1.3833

6.5573E + 00

2.1558

4.2076E + 00

3.4790

2.6073E + 00

76

1.3833

6.5573E + 00

2.1558

4.2076E + 00

3.4789

2.6073E + 00

77

1.3833

6.5573E + 00

2.1558

4.2076E + 00

3.4789

2.6074E + 00

78

1.3833

6.5573E + 00

2.1558

4.2076E + 00

3.4789

2.6074E + 00