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

n × 100	t	\(\|\mathcal{E}_{1}-\mathcal{E}_{0.94}\|\)	\(\|\mathcal{E}_{1}-\mathcal{E}_{0.96}\|\)	\(\|\mathcal{E}_{1}-\mathcal{E}_{0.98}\|\)	\(\|\mathcal{E}_{1}-\mathcal{E}_{0.998}\|\)
0	0	0.0000	0.0000	0.0000	0.0000
1	10	2.3330	1.5683	0.7911	0.0798
2	20	2.3304	1.5394	0.7615	0.0753
3	30	1.6432	1.0617	0.5124	0.0494
4	40	1.1764	0.7514	0.3586	0.0342
5	50	0.9012	0.5763	0.2766	0.0266
6	60	0.7311	0.4719	0.2306	0.0228
7	70	0.6169	0.4034	0.2019	0.0207
8	80	0.5343	0.3540	0.1818	0.0194
9	90	0.4711	0.3159	0.1663	0.0186
10	100	0.4206	0.2850	0.1533	0.0179
11	110	0.3792	0.2591	0.1421	0.0174
12	120	0.3446	0.2370	0.1320	0.0168
13	130	0.3153	0.2180	0.1230	0.0163
14	140	0.2900	0.2014	0.1149	0.0157
15	150	0.2681	0.1869	0.1076	0.0152
16	160	0.2490	0.1740	0.1009	0.0147
17	170	0.2321	0.1626	0.0949	0.0142
18	180	0.2170	0.1524	0.0894	0.0136
19	190	0.2036	0.1433	0.0844	0.0132
20	200	0.1915	0.1350	0.0798	0.0127