Theory and Modern Applications
Table 2 The results obtained for Example 3.4 for different values of α
From: Theories and applications of the inverse fractional natural transform method
x | t | α = 0.25 | α = 0.5 | α = 0.75 | α = 1 | |
|---|---|---|---|---|---|---|
Numerical | Exact | |||||
0.5 | 0.001 | 1.64621 | 1.64557 | 1.64545 | 1.64543 | 1.64543 |
0.003 | 1.63568 | 1.6396 | 1.63898 | 1.63886 | 1.63886 | |
0.005 | 1.62066 | 1.63386 | 1.63261 | 1.63232 | 1.63232 | |
1 | 0.001 | 2.71414 | 2.71309 | 2.71288 | 2.71285 | 2.71285 |
0.003 | 2.69678 | 2.70324 | 2.70223 | 2.70202 | 2.70202 | |
0.005 | 2.67201 | 2.69379 | 2.69172 | 2.69123 | 2.69123 | |
1.5 | 0.001 | 4.47487 | 4.47314 | 4.47279 | 4.47273 | 4.47273 |
0.003 | 4.44623 | 4.45688 | 4.45522 | 4.45488 | 4.45488 | |
0.005 | 4.4054 | 4.4413 | 4.4379 | 4.4371 | 4.4371 | |
2 | 0.001 | 7.37781 | 7.37495 | 7.37438 | 7.37429 | 7.37429 |
0.003 | 7.3306 | 7.34816 | 7.34542 | 7.34485 | 7.34485 | |
0.005 | 7.26328 | 7.32247 | 7.31686 | 7.31553 | 7.31553 | |