Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Solutions of system (12) with the comparison to GL and ABM for \(\sigma = 0.95\), \(\alpha = 0.6\)

t	LFFRK		GL [15]		ABM [38]
t	\([ \tilde{x} ( t ) ]^{\alpha } \)	\([ \tilde{y} ( t ) ]^{\alpha } \)	\([ \tilde{x} ( t ) ]^{\alpha } \)	\([ \tilde{y} ( t ) ]^{\alpha } \)	\([ \tilde{x} ( t ) ]^{\alpha } \)	\([ \tilde{y} ( t ) ]^{\alpha } \)
0.0	[0.4200, 0.6600]	[0.4600, 0.5800]	[0.4200, 0.6600]	[0.4600, 0.5800]	[0.4200, 0.6600]	[0.4600, 0.5800]
0.1	[0.4042, 0.6362]	[0.4689, 0.5969]	[0.4025, 0.6371]	[0.4694, 0.5996]	[0.4016, 0.6324]	[0.4704, 0.5995]
0.2	[0.3888, 0.6131]	[0.4777, 0.6136]	[0.3859, 0.6152]	[0.4777, 0.6175]	[0.3838, 0.6057]	[0.4805, 0.6186]
0.3	[0.3738, 0.5907]	[0.4863, 0.6300]	[0.3701, 0.5944]	[0.4855, 0.6347]	[0.3667, 0.5799]	[0.4903, 0.6375]
0.4	[0.3593, 0.5690]	[0.4946, 0.6462]	[0.3549, 0.5744]	[0.4929, 0.6515]	[0.3501, 0.5551]	[0.4999, 0.6559]
0.5	[0.3453, 0.5480]	[0.5027, 0.6620]	[0.3402, 0.5552]	[0.4999, 0.6679]	[0.3341, 0.5311]	[0.5091, 0.6741]
0.6	[0.3317, 0.5277]	[0.5106, 0.6776]	[0.3262, 0.5366]	[0.5068, 0.6841]	[0.3187, 0.5081]	[0.5181, 0.6918]
0.7	[0.3186, 0.5081]	[0.5183, 0.6929]	[0.3126, 0.5188]	[0.5133, 0.6999]	[0.3039, 0.4859]	[0.5267, 0.7091]
0.8	[0.3059, 0.4890]	[0.5257, 0.7078]	[0.2996, 0.5015]	[0.5196, 0.7154]	[0.2898, 0.4647]	[0.5350, 0.7259]
0.9	[0.2937, 0.4707]	[0.5329, 0.7224]	[0.2869, 0.4849]	[0.5257, 0.7306]	[0.2762, 0.4443]	[0.5431, 0.7422]
1.0	[0.2819, 0.4529]	[0.5399, 0.7366]	[0.2748, 0.4688]	[0.5315, 0.7455]	[0.2632, 0.4247]	[0.5508, 0.7581]