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Theory and Modern Applications

Table 2 Some numerical results for calculation of \(\varGamma _{q}(x)\) with \(q=\frac{1}{3}, \frac{1}{2}, \frac{2}{3}\), \(x=5\) and \(n=1, 2, \ldots , 35\) of Algorithm 2

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

n

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

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

\(q=\frac{2}{3}\)

n

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

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

\(q=\frac{2}{3}\)

1

3.016535

6.291859

18.937427

18

2.853224

4.921884

8.476643

2

2.906140

5.548726

14.154784

19

2.853224

4.921879

8.474597

3

2.870699

5.222330

11.819974

20

2.853224

4.921877

8.473234

4

2.859031

5.069033

10.537540

21

2.853224

4.921876

8.472325

5

2.855157

4.994707

9.782069

22

2.853224

4.921876

8.471719

6

2.853868

4.958107

9.317265

23

2.853224

4.921875

8.471315

7

2.853438

4.939945

9.023265

24

2.853224

4.921875

8.471046

8

2.853295

4.930899

8.833940

25

2.853224

4.921875

8.470866

9

2.853247

4.926384

8.710584

26

2.853224

4.921875

8.470747

10

2.853232

4.924129

8.629588

27

2.853224

4.921875

8.470667

11

2.853226

4.923002

8.576133

28

2.853224

4.921875

8.470614

12

2.853224

4.922438

8.540736

29

2.853224

4.921875

8.470578

13

2.853224

4.922157

8.517243

30

2.853224

4.921875

8.470555

14

2.853224

4.922016

8.501627

31

2.853224

4.921875

8.470539

15

2.853224

4.921945

8.491237

32

2.853224

4.921875

8.470529

16

2.853224

4.921910

8.484320

33

2.853224

4.921875

8.470522

17

2.853224

4.921893

8.479713

34

2.853224

4.921875

8.470517