Theory and Modern Applications
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 |