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Theory and Modern Applications

Table 3 Some numerical results for calculation of \(\varGamma _{q}(x)\) with \(x=8.4\), \(q=\frac{1}{3}, \frac{1}{2}, \frac{2}{3}\), and \(n=1, 2, \ldots, 40\) of Algorithm 2

From: Solutions of two fractional q-integro-differential equations under sum and integral boundary value conditions on a time scale

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

11.909360

63.618604

664.767669

21

11.257063

49.065390

260.033372

2

11.468397

55.707508

474.800503

22

11.257063

49.065384

260.011354

3

11.326853

52.245122

384.795341

23

11.257063

49.065381

259.996678

4

11.280255

50.621828

336.326796

24

11.257063

49.065380

259.986893

5

11.264786

49.835472

308.146441

25

11.257063

49.065379

259.980371

6

11.259636

49.448420

290.958806

26

11.257063

49.065379

259.976023

7

11.257921

49.256401

280.150029

27

11.257063

49.065379

259.973124

8

11.257349

49.160766

273.216364

28

11.257063

49.065378

259.971192

9

11.257158

49.113041

268.710272

29

11.257063

49.065378

259.969903

10

11.257095

49.089202

265.756606

30

11.257063

49.065378

259.969044

11

11.257074

49.077288

263.809514

31

11.257063

49.065378

259.968472

12

11.257066

49.071333

262.521127

32

11.257063

49.065378

259.968090

13

11.257064

49.068355

261.666471

33

11.257063

49.065378

259.967836

14

11.257063

49.066867

261.098587

34

11.257063

49.065378

259.967666

15

11.257063

49.066123

260.720833

35

11.257063

49.065378

259.967553

16

11.257063

49.065751

260.469369

36

11.257063

49.065378

259.967478

17

11.257063

49.065564

260.301890

37

11.257063

49.065378

259.967427

18

11.257063

49.065471

260.190310

38

11.257063

49.065378

259.967394

19

11.257063

49.065425

260.115957

39

11.257063

49.065378

259.967371

20

11.257063

49.065402

260.066402

40

11.257063

49.065378

259.967357