Table 5 The numerical results with the published work for \(M,\,\,K, \mathrm{and\,\, \phi }=0\).

	Wang⁴⁷		Abel et al.⁴⁸		Li et al.⁴⁶		Present
S	\(\beta\)	\(f^{\prime\prime}\left( 0 \right)\)	\(\beta\)	\(f^{\prime\prime}\left( 0 \right)\)	\(\beta\)	\(f^{\prime\prime}\left( 0 \right)\)	\(\beta\)	\(f^{\prime\prime}\left( 0 \right)\)
0.4	5.12249	− 1.30778	4.98146	− 1.13409	4.98146	− 1.134	4.98147	− 1.13409
0.6	3.13125	− 1.19516	3.13171	− 1.19513	3.13192	− 1.195	3.13171	− 1.19512
0.8	2.15199	− 1.24579	2.15199	− 1.24580	2.15237	− 1.246	2.15202	− 1.24581
1.0	1.54362	− 1.27776	1.54362	− 1.27777	1.54359	− 1.278	1.54362	− 1.27777
1.2	1.12778	− 1.27918	1.12278	− 1.27917	1.12778	− 1.279	1.12778	− 1.27917
1.4	0.82103	− 1.23355	0.82210	− 1.23354	0.82103	− 1.234	0.82103	− 1.23354
1.6	0.57617	− 1.11494	0.57617	− 1.11494	0.57617	− 1.115	0.57617	1.114937
1.8	0.35639	− 0.86741	0.35639	− 0.86742	0.35639	− 0.8674	0.35639	0.867410

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