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

n × 100	t	\(\|\mathcal{R}_{1}-\mathcal{R}_{0.94}\|\)	\(\|\mathcal{R}_{1}-\mathcal{R}_{0.96}\|\)	\(\|\mathcal{R}_{1}-\mathcal{R}_{0.98}\|\)	\(\|\mathcal{R}_{1}-\mathcal{R}_{0.998}\|\)
0	0	0.0000	0.0000	0.0000	0.0000
1	10	0.2888	0.2104	0.1142	0.0122
2	20	1.5940	1.0751	0.5428	0.0547
3	30	1.1569	0.7549	0.3678	0.0357
4	40	0.7942	0.5076	0.2421	0.0230
5	50	0.5826	0.3703	0.1761	0.0168
6	60	0.4574	0.2922	0.1407	0.0137
7	70	0.3772	0.2435	0.1197	0.0120
8	80	0.3215	0.2102	0.1059	0.0110
9	90	0.2802	0.1854	0.0957	0.0104
10	100	0.2481	0.1659	0.0875	0.0100
11	110	0.2223	0.1499	0.0806	0.0096
12	120	0.2010	0.1365	0.0746	0.0092
13	130	0.1831	0.1250	0.0693	0.0089
14	140	0.1679	0.1152	0.0646	0.0086
15	150	0.1548	0.1066	0.0603	0.0083
16	160	0.1434	0.0990	0.0565	0.0080
17	170	0.1334	0.0924	0.0530	0.0077
18	180	0.1245	0.0864	0.0499	0.0074
19	190	0.1166	0.0811	0.0470	0.0072
20	200	0.1096	0.0764	0.0444	0.0069