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Theory and Modern Applications

Table 9 The values of \(\vert \mathcal{A}_{1} - \mathcal{A}_{\phi } \vert \) for \(\phi = \{0.94, 0.96, 0.98, 0.998\}\)

From: On analysis of a nonlinear fractional system for social media addiction involving Atangana–Baleanu–Caputo derivative

n × 100

t

\(|\mathcal{A}_{1}-\mathcal{A}_{0.94}|\)

\(|\mathcal{A}_{1}-\mathcal{A}_{0.96}|\)

\(|\mathcal{A}_{1}-\mathcal{A}_{0.98}|\)

\(|\mathcal{A}_{1}-\mathcal{A}_{0.998}|\)

0

0

0.0000

0.0000

0.0000

0.0000

1

10

0.8805

0.5864

0.2929

0.0293

2

20

0.7437

0.4835

0.2354

0.0229

3

30

0.4924

0.3122

0.1479

0.0140

4

40

0.3401

0.2125

0.0991

0.0093

5

50

0.2546

0.1587

0.0742

0.0070

6

60

0.2034

0.1277

0.0606

0.0058

7

70

0.1700

0.1080

0.0523

0.0052

8

80

0.1463

0.0941

0.0467

0.0048

9

90

0.1285

0.0836

0.0425

0.0046

10

100

0.1144

0.0751

0.0390

0.0044

11

110

0.1030

0.0682

0.0360

0.0042

12

120

0.0935

0.0623

0.0334

0.0041

13

130

0.0855

0.0572

0.0311

0.0039

14

140

0.0786

0.0529

0.0290

0.0038

15

150

0.0727

0.0490

0.0272

0.0037

16

160

0.0675

0.0457

0.0255

0.0035

17

170

0.0629

0.0427

0.0240

0.0034

18

180

0.0589

0.0400

0.0226

0.0033

19

190

0.0553

0.0376

0.0213

0.0032

20

200

0.0521

0.0355

0.0202

0.0031