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 5 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	0.3700	0.2530	0.1293	0.0131
2	20	1.2369	0.8260	0.4129	0.0412
3	30	0.9083	0.5816	0.2778	0.0265
4	40	0.5125	0.3109	0.1399	0.0126
5	50	0.2899	0.1675	0.0717	0.0062
6	60	0.1759	0.0986	0.0411	0.0035
7	70	0.1164	0.0644	0.0267	0.0023
8	80	0.0832	0.0460	0.0192	0.0016
9	90	0.0632	0.0352	0.0148	0.0013
10	100	0.0504	0.0282	0.0120	0.0010
11	110	0.0415	0.0235	0.0100	0.0009
12	120	0.0352	0.0200	0.0086	0.0008
13	130	0.0304	0.0174	0.0075	0.0007
14	140	0.0267	0.0153	0.0066	0.0006
15	150	0.0238	0.0137	0.0059	0.0005
16	160	0.0214	0.0123	0.0054	0.0005
17	170	0.0194	0.0112	0.0049	0.0004
18	180	0.0178	0.0103	0.0045	0.0004
19	190	0.0164	0.0095	0.0042	0.0004
20	200	0.0152	0.0088	0.0039	0.0003