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 5 Solutions of system (15) 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	[0.3939, 0.6453]	[0.4775, 0.5883]	[0.3929, 0.6455]	[0.4793, 0.5897]	[0.3899, 0.6428]	[0.4801, 0.5897]
0.2	[0.3682, 0.6315]	[0.4949, 0.5962]	[0.3670, 0.6318]	[0.4971, 0.5978]	[0.3603, 0.6266]	[0.5001, 0.5989]
0.3	[0.3429, 0.6184]	[0.5121, 0.6038]	[0.3421, 0.6191]	[0.5142, 0.6054]	[0.3313, 0.6114]	[0.5198, 0.6077]
0.4	[0.3181, 0.6061]	[0.5291, 0.6111]	[0.3178, 0.6072]	[0.5308, 0.6126]	[0.3029, 0.5974]	[0.5393, 0.6159]
0.5	[0.2936, 0.5947]	[0.5459, 0.6178]	[0.2942, 0.5962]	[0.5472, 0.6193]	[0.2750, 0.5844]	[0.5586, 0.6237]
0.6	[0.2695, 0.5842]	[0.5627, 0.6242]	[0.2710, 0.5859]	[0.5632, 0.6256]	[0.2476, 0.5727]	[0.5776, 0.6308]
0.7	[0.2457, 0.5746]	[0.5792, 0.6301]	[0.2483, 0.5766]	[0.5790, 0.6314]	[0.2206, 0.5621]	[0.5964, 0.6373]
0.8	[0.2222, 0.5659]	[0.5956, 0.6354]	[0.2259, 0.5680]	[0.5946, 0.6368]	[0.1939, 0.5527]	[0.6149, 0.6431]
0.9	[0.1989, 0.5580]	[0.6118, 0.6403]	[0.2040, 0.5602]	[0.6100, 0.6417]	[0.1677, 0.5446]	[0.6334, 0.6482]
1.0	[0.1759, 0.5513]	[0.6279, 0.6445]	[0.1823, 0.5533]	[0.6252, 0.6462]	[0.1418, 0.5378]	[0.6517, 0.6525]