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

n × 100	t	\(\|\mathcal{A}_{1}-\mathcal{A}_{0.94}\|\)	\(\|\mathcal{A}_{1}-\mathcal{A}_{0.96}\|\)	\(\|\mathcal{A}_{1}-\mathcal{A}_{0.98}\|\)	\(\|\mathcal{A}_{1}-\mathcal{A}_{0.998}\|\)
0	0	0.0000	0.0000	0.0000	0.0000
1	10	0.4406	0.2808	0.1338	0.0128
2	20	0.6111	0.3939	0.1900	0.0184
3	30	0.3656	0.2257	0.1039	0.0096
4	40	0.1999	0.1171	0.0509	0.0044
5	50	0.1139	0.0638	0.0265	0.0022
6	60	0.0706	0.0386	0.0157	0.0013
7	70	0.0479	0.0260	0.0106	0.0009
8	80	0.0351	0.0191	0.0079	0.0007
9	90	0.0273	0.0150	0.0062	0.0005
10	100	0.0222	0.0123	0.0051	0.0004
11	110	0.0186	0.0104	0.0044	0.0004
12	120	0.0160	0.0090	0.0038	0.0003
13	130	0.0140	0.0079	0.0034	0.0003
14	140	0.0124	0.0070	0.0030	0.0003
15	150	0.0112	0.0063	0.0027	0.0002
16	160	0.0101	0.0058	0.0025	0.0002
17	170	0.0093	0.0053	0.0023	0.0002
18	180	0.0086	0.0049	0.0021	0.0002
19	190	0.0079	0.0045	0.0020	0.0002
20	200	0.0074	0.0042	0.0018	0.0002