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 3 Solutions of system (13) 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	[0.4064, 0.6329]	[0.4774, 0.5884]	[0.4048, 0.6337]	[0.4789, 0.5898]	[0.4042, 0.6284]	[0.4802, 0.5897]
0.2	[0.3929, 0.6068]	[0.4943, 0.5968]	[0.3901, 0.6088]	[0.4961, 0.5985]	[0.3888, 0.5982]	[0.4997, 0.5993]
0.3	[0.3798, 0.5817]	[0.5106, 0.6050]	[0.3761, 0.5853]	[0.5123, 0.6069]	[0.3737, 0.5692]	[0.5185, 0.6087]
0.4	[0.3670, 0.5575]	[0.5265, 0.6132]	[0.3625, 0.5628]	[0.5278, 0.6151]	[0.3590, 0.5415]	[0.5367, 0.6181]
0.5	[0.3545, 0.5342]	[0.5419, 0.6212]	[0.3493, 0.5413]	[0.5427, 0.6230]	[0.3447, 0.5151]	[0.5542, 0.6273]
0.6	[0.3423, 0.5118]	[0.5568, 0.6291]	[0.3366, 0.5208]	[0.5571, 0.6308]	[0.3309, 0.4898]	[0.5711, 0.6363]
0.7	[0.3304, 0.4903]	[0.5712, 0.6369]	[0.3243, 0.5009]	[0.5709, 0.6384]	[0.3175, 0.4657]	[0.5873, 0.6451]
0.8	[0.3189, 0.4696]	[0.5852, 0.6445]	[0.3123, 0.4820]	[0.5843, 0.6458]	[0.3045, 0.4427]	[0.6029, 0.6536]
0.9	[0.3077, 0.4497]	[0.5987, 0.6519]	[0.3008, 0.4638]	[0.5972, 0.6531]	[0.2919, 0.4207]	[0.6179, 0.6619]
1.0	[0.2968, 0.4307]	[0.6117, 0.6591]	[0.2896, 0.4462]	[0.6097, 0.6602]	[0.2799, 0.3998]	[0.6322, 0.6701]