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Theory and Modern Applications

Table 3 Numerical results of \(\Gamma _{q}(\sigma +1)\), Δ, and \(\ell < \frac{\Gamma _{q} ( 2 - \varsigma )}{\Delta [ 3 + \Gamma _{q} ( 2 - \varsigma )] }\) for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.2 (Algorithm 2)

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

n

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

Δ

â„“

 

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

1

1.3187

7.3233E + 00

1.3655E − 01

2

1.3084

7.3811E + 00

1.3548E − 01

3

1.3063

7.3927E + 00

1.3527E − 01

4

1.3059

7.3950E + 00

1.3523E − 01

5

1.3058

7.3954E + 00

1.3522E − 01

6

1.3058

7.3955E + 00

1.3522E − 01

 

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

1

2.2951

4.2077E + 00

2.3766E − 01

2

2.0569

4.6949E + 00

2.1300E − 01

3

1.9515

4.9486E + 00

2.0208E − 01

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â‹®

â‹®

â‹®

10

1.8546

5.2070E + 00

1.9205E − 01

11

1.8543

5.2080E + 00

1.9201E − 01

12

1.8541

5.2086E + 00

1.9199E − 01

13

1.8540

5.2088E + 00

1.9198E − 01

14

\( \underline{1}\underline{.}\underline{8539} \)

5.2089E + 00

1.9198E − 01

15

1.8539

5.2090E + 00

1.9198E − 01

16

1.8539

5.2090E + 00

1.9197E − 01

 

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

1

26.5678

3.6349E − 01

2.7511E + 00

2

17.0689

5.6577E − 01

1.7675E + 00

3

12.2939

7.8552E − 01

1.2731E + 00

4

9.5395

1.0123E + 00

9.8783E − 01

5

7.7985

1.2383E + 00

8.0755E − 01

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80

2.6759

3.6089E + 00

2.7709E − 01

81

2.6759

3.6090E + 00

2.7709E − 01

82

\( \underline{2}\underline{.}\underline{6758} \)

3.6090E + 00

2.7709E − 01

83

2.6758

3.6090E + 00

2.7709E − 01

84

2.6758

3.6090E + 00

2.7709E − 01

85

2.6758

3.6090E + 00

2.7708E − 01

86

2.6758

3.6090E + 00

2.7708E − 01

87

2.6758

3.6090E + 00

2.7708E − 01

88

2.6758

3.6090E + 00

2.7708E − 01