Theory and Modern Applications
Table 4 Results for \(\alpha >0\) with the fixed value \(\beta =1\) of Case 6.2
α | Γ(α + 2) | Γ(α + 1) | \(\frac{{\alpha c}_{{1}}}{{\varGamma } ( {\alpha }+{2} )} {D} [ {1}- ( \frac{{D}}{{K}} )^{\frac{{1}}{{\alpha }}} ] = {c}_{{2}}\) | \({T}^{{*}}\) | \({\mathrm{TAC}}^{{*}}\) | \({q}_{{max}}^{{*}}\) |
|---|---|---|---|---|---|---|
0.1 | 1.04648585469 | 0.9135076987 | 458.3802 | 0.6801931 | 319.2005 | 631.1130 |
0.2 | 1.10180249088 | 0.9181687424 | 879.0985 | 0.2358365 | 446.3459 | 509.0779 |
0.3 | 1.16671190520 | 0.8974706963 | 1127.364 | 0.1551386 | 480.7231 | 397.5395 |
0.4 | 1.24216934450 | 0.8872638175 | 1298.952 | 0.1304171 | 476.9366 | 311.3620 |
0.5 | 1.32934038818 | 0.8862269255 | 1389.441 | 0.1230857 | 460.6260 | 247.0264 |
0.6 | 1.42962455886 | 0.8935153493 | 1421.718 | 0.1234093 | 441.9322 | 199.0175 |
0.7 | 1.54468584585 | 0.9086387329 | 1412.893 | 0.1279405 | 414.5195 | 162.8167 |
0.8 | 1.67649078776 | 0.9313837710 | 1375.371 | 0.1351746 | 409.5117 | 135.1363 |
0.9 | 1.82735508062 | 0.9617658319 | 1318.186 | 0.1443518 | 397.0645 | 113.6567 |
1 | 2.00000000000 | 1.0000000000 | 1248.000 | 0.1550434 | 386.9884 | 96.74709 |