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 2 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	0.7861	0.5441	0.2809	0.0287
2	20	0.7332	0.5485	0.3071	0.0339
3	30	0.8142	0.6232	0.3560	0.0399
4	40	0.8049	0.6112	0.3452	0.0383
5	50	0.7067	0.5238	0.2879	0.0311
6	60	0.5638	0.4032	0.2132	0.0222
7	70	0.4087	0.2778	0.1387	0.0136
8	80	0.2593	0.1614	0.0719	0.0061
9	90	0.1236	0.0591	0.0150	0.0000
10	100	0.0041	0.0287	0.0326	0.0051
11	110	0.0999	0.1033	0.0722	0.0092
12	120	0.1898	0.1666	0.1051	0.0126
13	130	0.2675	0.2205	0.1327	0.0154
14	140	0.3350	0.2666	0.1560	0.0177
15	150	0.3939	0.3063	0.1759	0.0197
16	160	0.4454	0.3408	0.1930	0.0214
17	170	0.4909	0.3709	0.2079	0.0228
18	180	0.5313	0.3975	0.2209	0.0241
19	190	0.5673	0.4211	0.2323	0.0252
20	200	0.5996	0.4421	0.2425	0.0262