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Theory and Modern Applications

Table 6 Some numerical results for calculation of \(\varLambda _{1}\) and \(\varLambda _{2}\) with \(q=\frac{3}{4}\) and \(n=1, 2, \ldots , 30\) of Example 2

From: New approach to solutions of a class of singular fractional q-differential problem via quantum calculus

n

\(\varGamma _{q}(2-\beta )\)

\(\varGamma _{q}(\alpha -\beta )\)

\(\varGamma _{q}(\alpha )\)

\(\varLambda _{1}\)

\(\varLambda _{2}\)

2

1.253179

1.462857

1.751525

−0.705095

−0.558789

3

1.149887

1.31114

1.536689

−0.807011

−0.644426

4

1.084407

1.216513

1.40468

−0.886016

−0.712105

5

1.040678

1.154047

1.318456

−0.946732

−0.764915

6

1.010469

1.111251

1.259837

−0.993102

−0.805725

7

0.989113

1.08118

1.218879

−1.028354

−0.83703

8

0.973772

1.059674

1.189708

−1.055062

−0.860912

9

0.962624

1.044098

1.168644

−1.075245

−0.879054

10

0.954455

1.032713

1.153282

−1.090469

−0.892792

11

0.948434

1.024335

1.141999

−1.101936

−0.903171

12

0.943976

1.018141

1.133666

−1.110563

−0.910997

13

0.940664

1.013544

1.127488

−1.117049

−0.916891

14

0.938198

1.010124

1.122894

−1.121923

−0.921325

15

0.936358

1.007574

1.119471

−1.125583

−0.924658

16

0.934984

1.00567

1.116915

−1.12833

−0.927162

17

0.933956

1.004246

1.115006

−1.130393

−0.929043

18

0.933187

1.003181

1.113578

−1.13194

−0.930455

19

0.932611

1.002384

1.112509

−1.133102

−0.931514

20

0.93218

1.001787

1.111708

−1.133973

−0.932309

21

0.931857

1.00134

1.111109

−1.134627

−0.932906

22

0.931615

1.001004

1.110659

−1.135117

−0.933354

23

0.931433

1.000753

1.110322

−1.135485

−0.933689

24

0.931297

1.000565

1.11007

−1.13576

−0.933941

25

0.931195

1.000423

1.10988

−1.135967

−0.93413

26

0.931118

1.000318

1.109738

−1.136122

−0.934272

27

0.931061

1.000238

1.109632

−1.136239

−0.934378

28

0.931018

1.000179

1.109552

−1.136326

−0.934458

29

0.930986

1.000134

1.109492

−1.136392

−0.934518

30

0.930961

1.0001

1.109447

−1.136441

−0.934562