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Table 1 Comparison of the numerical solution for \(\pmb{\nu=1.5}\) , \(\pmb{\alpha =0.5, 1}\) , and \(\pmb{M=17}\) with other results in [ 23 , 27 ]

From: A fractional-order Legendre collocation method for solving the Bagley-Torvik equations

t Exact FSLPs ( α  = 0.5) FSLPs ( α  = 1.0) Ref. [ 27 ] Ref. [ 23 ]
1.40625 4.85696 4.80915 4.85715 4.95531 4.67105
2.03125 6.83165 6.78579 6.85062 6.93440 6.48436
2.96875 7.67925 7.64470 7.67261 7.80605 7.21918
3.59375 6.97278 6.94967 6.98356 7.09830 6.51938
4.21875 5.48313 5.47278 5.48883 5.59310 5.09093
5.46875 1.28657 1.29947 1.28343 1.33675 1.11881
7.96875 −4.53369 −4.50974 −4.53926 −4.59731 −4.30082
9.53125 −3.64404 −3.63542 −3.64279 −3.71142 −3.40603
11.7188 0.59143 0.57883 0.59421 0.58569 0.61398
13.5938 2.64127 2.62760 2.63996 2.67926 2.51628
15.4688 1.72175 1.71945 1.72207 1.75636 1.60585
16.4063 0.63025 0.63383 0.62882 0.64944 0.56273
17.3438 −0.44428 −0.43668 −0.44270 −0.44298 −0.45529
18.9063 −1.50186 −1.49344 −1.49966 −1.52298 −1.44138
19.8438 −1.52304 −1.51713 −1.518921 −1.54859 −1.44734