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Journal of Inequalities and Applications

Table 5 Numerical results of \(\Gamma _{q}(\sigma -2)\), \(\Gamma _{q}(\zeta )\), and \(\Lambda = \frac{1+ (\sigma -2) \Gamma _{q}( \zeta ) }{\Gamma _{q}( \sigma -2) \Gamma _{q}(\zeta ) }\) in equation (62) for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.3

From: The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach

n

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

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

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

\(\Gamma _{q}(\sigma -2)\)

\(\Gamma _{q}(\zeta )\)

Λ

\(\Gamma _{q}(\sigma -2)\)

\(\Gamma _{q}(\zeta )\)

Λ

\(\Gamma _{q}(\sigma -2)\)

\(\Gamma _{q}(\zeta )\)

Λ

1

1.2612

1.0573

1.2030

1.2839

1.0584

1.1809

0.8642

0.9059

1.9386

2

1.2714

1.0600

1.1915

1.3507

1.0773

1.1103

0.9815

0.9493

1.6555

3

1.2734

1.0605

1.1892

1.3826

1.0861

1.0792

1.0708

0.9805

1.4860

4

1.2738

1.0606

1.1888

1.3982

1.0905

1.0646

1.1416

1.0043

1.3727

5

1.2739

1.0606

1.4059

1.0926

1.0575

1.1991

1.0231

1.2917

6

1.2739

1.0606

1.1887

1.4097

1.0936

1.0540

1.2466

1.0382

1.2311

7

1.2739

1.0606

1.1887

1.4116

1.0942

1.0522

1.2863

1.0506

1.1843

8

1.2739

1.0606

1.1887

1.4126

1.0944

1.0514

1.3197

1.0608

1.1473

9

1.2739

1.0606

1.1887

1.4131

1.0945

1.0509

1.3480

1.0694

1.1176

10

1.2739

1.0606

1.1887

1.4133

1.0946

1.0507

1.3722

1.0767

1.0933

11

1.2739

1.0606

1.1887

1.4134

1.0946

1.0506

1.3929

1.0828

1.0733

12

1.2739

1.0606

1.1887

1.4135

1.0947

1.4106

1.0881

1.0566

13

1.2739

1.0606

1.1887

1.4135

1.0947

1.0505

1.4260

1.0925

1.0426

14

1.2739

1.0606

1.1887

1.4135

1.0947

1.0505

1.4392

1.0964

1.0308

15

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.4506

1.0997

1.0208

16

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.4605

1.1026

1.0122

⋮

⋮

⋮

⋮

⋮

⋮

⋮

⋮

⋮

⋮

51

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5269

1.1214

0.9582

52

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5270

1.1215

0.9582

53

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5271

1.1215

0.9581

54

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5271

1.1215

0.9581

55

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5272

1.1215

0.9580

56

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5272

1.1215

0.9580

57

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5273

1.1215

0.9580

58

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5273

1.1215

59

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5273

1.1216

0.9579

60

1.2739

1.0606

1.1887

1.4136

1.0947

1.0505

1.5273

1.1216

0.9579

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