Table 4 Numerical results for finding suitable values of η in equation (27) for \(q = \frac{1}{5}\), \(\frac{1}{2}\), \(\frac{7}{8}\) in Example 4.2, where \(\Omega (\eta )= [ \phi _{1}(\eta ) + \phi _{2}(\eta ) +1 ] ( M_{1} + \frac{M_{2}}{(1 - \zeta ) \Gamma _{q} (1 - \zeta )} ) -\eta \)
n | η | Ω(η)<0 | ||
|---|---|---|---|---|
\(q = \frac{1}{ 5}\) | \(q = \frac{ 1}{ 2}\) | \(q = \frac{7}{8}\) | ||
1 | 3.0000 | 2.1347 | 0.9079 | 0.0906 |
2 | 3.1000 | 2.1154 | 0.8693 | 0.0392 |
3 | 3.2000 | 2.0943 | 0.8294 |
|
4 | 3.3000 | 2.0715 | 0.7882 | −0.0668 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
9 | 3.8000 | 1.9351 | 0.5649 | −0.3480 |
10 | 3.9000 | 1.9036 | 0.5170 | −0.4068 |
11 | 4.0000 | 1.8708 | 0.4681 | −0.4663 |
12 | 4.1000 | 1.8367 | 0.4183 | −0.5266 |
13 | 4.2000 | 1.8014 | 0.3676 | −0.5877 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
18 | 4.7000 | 1.6077 | 0.1007 | −0.9033 |
19 | 4.8000 | 1.5658 | 0.0449 | −0.9684 |
20 | 4.9000 | 1.5229 |
| −1.0340 |
21 | 5.0000 | 1.4790 | −0.0690 | −1.1002 |
22 | 5.1000 | 1.4342 | −0.1270 | −1.1670 |
23 | 5.2000 | 1.3884 | −0.1857 | −1.2344 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
47 | 7.6000 | 0.0745 | −1.7591 | −2.9806 |
48 | 7.7000 | 0.0126 | −1.8301 | −3.0577 |
49 | 7.8000 |
| −1.9015 | −3.1351 |
50 | 7.9000 | −0.1126 | −1.9732 | −3.2127 |
51 | 8.0000 | −0.1759 | −2.0452 | −3.2906 |
52 | 8.1000 | −0.2395 | −2.1176 | −3.3687 |
53 | 8.2000 | −0.3037 | −2.1903 | −3.4471 |
