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Theory and Modern Applications

Table 11 Numerical results of \((1)=L_{1} \varLambda _{1}+ |{}_{1}b_{0}|\) and \((i)=L_{i}\varLambda _{i} + \sum_{j=0}^{i-2} \frac{|{}_{i}b_{j}|}{j!}\) with \(2 \leq i \leq 5\) in Example 2 for \(q=\frac{1}{10}\)

From: An increasing variables singular system of fractional q-differential equations via numerical calculations

n

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

r

(1)

(2)

(3)

(4)

(5)

1

0.0984

1.144

2.5911

4.4968

1.9969

4.4968

2

0.1106

1.1634

2.7596

4.5846

2.0093

4.5846

3

0.1166

1.1734

2.8485

4.6312

2.0162

4.6312

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â‹®

â‹®

â‹®

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7

0.1222

1.1828

2.9348

4.6767

2.023

4.6767

8

0.1224

1.1831

2.9377

4.6782

2.0233

4.6782

9

0.1225

1.1833

2.9392

4.679

2.0234

4.679

10

0.1225

1.1833

2.9399

4.6794

2.0234

4.6794

11

0.1226

1.1834

2.9403

4.6796

2.0235

4.6796

12

0.1226

1.1834

2.9404

4.6797

2.0235

4.6797

13

0.1226

1.1834

2.9405

4.6797

2.0235

4.6797

14

0.1226

1.1834

2.9406

4.6797

2.0235

4.6797

15

0.1226

1.1834

2.9406

2.0235

4.6798

16

0.1226

1.1834

2.9406

4.6798

2.0235

4.6798

17

0.1226

1.1834

2.9406

4.6798

2.0235

4.6798