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Theory and Modern Applications

Table 11 The values of \(\vert \mathcal{Q}_{1} - \mathcal{Q}_{\phi } \vert \) 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

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

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

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

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

0

0

0.0000

0.0000

0.0000

0.0000

1

10

5.1605

3.5009

1.7808

0.1808

2

20

4.2916

2.8933

1.4625

0.1477

3

30

1.2904

0.8236

0.3936

0.0378

4

40

0.6949

0.5294

0.2967

0.0323

5

50

1.7232

1.2216

0.6462

0.0676

6

60

2.1497

1.5028

0.7865

0.0817

7

70

2.2375

1.5545

0.8111

0.0844

8

80

2.1499

1.4882

0.7768

0.0813

9

90

1.9822

1.3688

0.7163

0.0758

10

100

1.7875

1.2322

0.6476

0.0696

11

110

1.5938

1.0972

0.5798

0.0636

12

120

1.4144

0.9727

0.5172

0.0581

13

130

1.2545

0.8621

0.4615

0.0532

14

140

1.1150

0.7658

0.4127

0.0490

15

150

0.9946

0.6828

0.3706

0.0453

16

160

0.8912

0.6118

0.3342

0.0421

17

170

0.8025

0.5509

0.3029

0.0393

18

180

0.7262

0.4986

0.2759

0.0368

19

190

0.6603

0.4535

0.2524

0.0346

20

200

0.6030

0.4144

0.2319

0.0326