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Table 4 Numerical results of \(\varpi _{i}\), \(i=1,2,3\), in Example 5.2 for three cases of derivative order α

From: Existence and stability of a q-Caputo fractional jerk differential equation having anti-periodic boundary conditions

n

\(\alpha = \frac {1}{8}\)

\(\alpha = \frac {1}{6}\)

\(\alpha = \frac {1}{3}\)

\(\varpi _{1}\)

\(\varpi _{2}\)

\(\varpi _{3}\)

\(\varpi _{1}\)

\(\varpi _{2}\)

\(\varpi _{3}\)

\(\varpi _{1}\)

\(\varpi _{2}\)

\(\varpi _{3}\)

1

2.222

1.941

1.896

2.156

1.887

1.857

1.898

1.673

1.692

2

3.084

2.372

1.961

3.017

2.325

1.942

2.736

2.125

1.841

3

3.656

2.628

1.995

3.592

2.588

1.986

3.309

2.403

1.921

4

4.018

2.782

2.013

3.957

2.745

2.010

3.677

2.572

1.966

5

4.243

2.874

2.024

4.183

2.839

2.024

3.907

2.674

1.992

6

4.380

2.929

2.030

4.322

2.896

2.032

4.049

2.736

2.007

7

4.463

2.962

2.034

4.406

2.930

2.037

4.134

2.773

2.016

8

4.513

2.981

2.036

4.456

2.950

2.040

4.186

2.795

2.021

9

4.543

2.993

2.037

4.487

2.963

2.041

4.218

2.808

2.025

10

4.561

3.000

2.038

4.505

2.970

2.042

4.237

2.816

2.027

11

4.572

3.005

2.038

4.516

2.974

2.043

4.248

2.821

2.028

12

4.578

3.007

2.038

4.523

2.977

2.043

4.255

2.824

2.028

13

4.582

3.009

2.039

4.527

2.979

2.043

4.259

2.826

2.029

14

4.585

3.010

2.039

4.529

2.980

2.044

4.261

2.827

2.029

15

4.586

3.010

2.039

4.531

2.980

2.044

4.263

2.827

2.029

16

4.587

3.011

2.039

4.532

2.980

2.044

4.264

2.828

2.029

17

4.588

3.011

2.039

4.532

2.981

2.044

4.264

2.828

2.029

18

4.588

3.011

2.039

4.532

2.981

2.044

4.264

2.828

2.029

19

4.588

3.011

2.039

4.533

2.981

2.044

4.265

2.828

2.029

20

4.588

3.011

2.039

4.533

2.981

2.044

4.265

2.828

2.029

21

4.588

3.011

2.039

4.533

2.981

2.044

4.265

2.828

2.029