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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 7 The values of \(\vert \mathcal{S}_{1} - \mathcal{S}_{\phi } \vert \) for \(\phi = \{0.94, 0.96, 0.98, 0.998\}\)

n × 100	t	\(\|\mathcal{S}_{1}-\mathcal{S}_{0.94}\|\)	\(\|\mathcal{S}_{1}-\mathcal{S}_{0.96}\|\)	\(\|\mathcal{S}_{1}-\mathcal{S}_{0.98}\|\)	\(\|\mathcal{S}_{1}-\mathcal{S}_{0.998}\|\)
0	0	0.0000	0.0000	0.0000	0.0000
1	10	0.3407	0.2299	0.1164	0.0118
2	20	0.1893	0.1422	0.0813	0.0093
3	30	0.1010	0.0570	0.0198	0.0008
4	40	0.4687	0.3241	0.1652	0.0164
5	50	0.7818	0.5588	0.2982	0.0313
6	60	1.0055	0.7317	0.4008	0.0435
7	70	1.1503	0.8474	0.4738	0.0529
8	80	1.2366	0.9190	0.5227	0.0601
9	90	1.2832	0.9595	0.5535	0.0654
10	100	1.3043	0.9790	0.5712	0.0693
11	110	1.3099	0.9851	0.5795	0.0721
12	120	1.3064	0.9828	0.5814	0.0740
13	130	1.2981	0.9759	0.5792	0.0753
14	140	1.2874	0.9664	0.5743	0.0759
15	150	1.2758	0.9558	0.5679	0.0761
16	160	1.2643	0.9449	0.5607	0.0760
17	170	1.2532	0.9342	0.5532	0.0757
18	180	1.2427	0.9241	0.5457	0.0752
19	190	1.2330	0.9145	0.5384	0.0745
20	200	1.2240	0.9056	0.5313	0.0738