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 4 Solutions of system (14) 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	[0.3973, 0.6431]	[0.4738, 0.5905]	[0.3964, 0.6432]	[0.4748, 0.5925]	[0.3938, 0.6402]	[0.4759, 0.5923]
0.2	[0.3748, 0.6271]	[0.4877, 0.6006]	[0.3737, 0.6275]	[0.4885, 0.6033]	[0.3680, 0.6215]	[0.4917, 0.6039]
0.3	[0.3526, 0.6121]	[0.5015, 0.6101]	[0.3517, 0.6128]	[0.5017, 0.6133]	[0.3426, 0.6040]	[0.5075, 0.6151]
0.4	[0.3307, 0.5979]	[0.5153, 0.6192]	[0.3302, 0.5992]	[0.5148, 0.6227]	[0.3176, 0.5877]	[0.5232, 0.6254]
0.5	[0.3090, 0.5846]	[0.5290, 0.6277]	[0.3092, 0.5865]	[0.5278, 0.6314]	[0.2929, 0.5726]	[0.5389, 0.6352]
0.6	[0.2876, 0.5723]	[0.5428, 0.6357]	[0.2884, 0.5747]	[0.5406, 0.6396]	[0.2685, 0.5588]	[0.5546, 0.6442]
0.7	[0.2662, 0.5609]	[0.5565, 0.6431]	[0.2679, 0.5638]	[0.5535, 0.6473]	[0.2443, 0.5461]	[0.5702, 0.6525]
0.8	[0.2451, 0.5505]	[0.5702, 0.6501]	[0.2477, 0.5538]	[0.5666, 0.6543]	[0.2204, 0.5348]	[0.5858, 0.6601]
0.9	[0.2241, 0.5410]	[0.5839, 0.6564]	[0.2277, 0.5446]	[0.5791, 0.6608]	[0.1966, 0.5247]	[0.6014, 0.6669]
1.0	[0.2031, 0.5325]	[0.5977, 0.6621]	[0.2078, 0.5363]	[0.5919, 0.6668]	[0.1730, 0.5159]	[0.6170, 0.6729]