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Theory and Modern Applications

Table 5 Numerical results of \(\mathcal{O}_{i}\) and \(\Lambda _{i}\), \(i=1,2,3\), for \(\mathfrak{t}\in [0.02,0.99]\) in Example 6.2 when \(q_{1}=0.28\), \(q_{2}=0.53\), and \(q_{3}=0.89\)

From: On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

 

\(q_{1} = 0.28\)

\(\mathfrak{t}\)

\(\mathcal{O}_{1}\)

\(\Lambda _{1}\)

\(\frac{B}{\Lambda _{1} + \mathcal{O}_{1} \varrho _{0}^{*} f (B)}> 1\)

0.02

0.000000

11.480000

8.710801

0.07

0.136126

14.719326

6.752573

0.12

0.269336

15.959688

6.196766

0.17

0.408139

16.987999

5.794625

0.22

0.553358

17.917221

5.469730

0.27

0.705303

18.788358

5.193764

0.32

0.864149

19.621462

4.952505

0.37

1.030023

20.427978

4.737587

0.42

1.203031

21.215104

4.543574

0.47

1.383268

21.987675

4.366692

0.52

1.570824

22.749106

4.204180

0.57

1.765784

23.501897

4.053948

0.62

1.968230

24.247935

3.914359

0.67

2.178243

24.988679

3.784106

0.72

2.395902

25.725280

3.662122

0.77

2.621284

26.458658

3.547520

0.82

2.854465

27.189562

3.439557

0.87

3.095519

27.918608

3.337600

0.92

3.344520

28.646309

3.241103

0.97

3.601540

29.373093

3.149595

1.02

3.866649

30.099324

3.062664