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

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	2.9460	1.9437	0.9588	0.0944
2	20	3.8530	2.6189	1.3357	0.1360
3	30	1.3208	0.8887	0.4509	0.0459
4	40	0.4132	0.2819	0.1407	0.0137
5	50	1.2436	0.8329	0.4154	0.0412
6	60	1.5414	1.0256	0.5100	0.0506
7	70	1.5670	1.0373	0.5142	0.0510
8	80	1.4662	0.9655	0.4768	0.0472
9	90	1.3159	0.8615	0.4231	0.0417
10	100	1.1551	0.7511	0.3665	0.0359
11	110	1.0025	0.6471	0.3134	0.0305
12	120	0.8661	0.5547	0.2663	0.0257
13	130	0.7480	0.4751	0.2261	0.0216
14	140	0.6476	0.4079	0.1924	0.0182
15	150	0.5630	0.3517	0.1644	0.0154
16	160	0.4921	0.3049	0.1412	0.0131
17	170	0.4326	0.2659	0.1221	0.0113
18	180	0.3825	0.2334	0.1063	0.0097
19	190	0.3402	0.2060	0.0931	0.0085
20	200	0.3042	0.1830	0.0820	0.0074