Table 2 RPS solutions and residual errors for the fuzzy-fractional HBV Model at \(\alpha =1\) and \(r=1\).
\(\alpha = 1,r = 1\) | |||||||
|---|---|---|---|---|---|---|---|
t | RPS solution \(\mathbb {S}(t)\) | RPS solution \(\mathbb {E}(t)\) | RPS solution \(\mathbb {I}(t)\) | RPS solution \(\mathbb {A}(t)\) | RPS solution \(\mathbb {C}(t)\) | RPS solution \(\mathbb {T}(t)\) | RPS solution \(\mathbb {R}(t)\) |
0. | 60. | 40. | 3. | 2. | 1. | 0. | 0. |
0.1 | 59.3593 | 40.6768 | 2.99297 | 1.9832 | 0.975024 | 0.0105487 | 0.0456291 |
0.2 | 58.7293 | 41.3427 | 2.98614 | 1.9667 | 0.950832 | 0.020801 | 0.0905297 |
0.3 | 58.1097 | 41.9977 | 2.97951 | 1.9505 | 0.927401 | 0.030766 | 0.134722 |
0.4 | 57.5003 | 42.6422 | 2.97306 | 1.93458 | 0.904705 | 0.0404525 | 0.178223 |
0.5 | 56.901 | 43.2765 | 2.96681 | 1.91896 | 0.882723 | 0.0498691 | 0.221054 |
0.6 | 56.3115 | 43.9006 | 2.96074 | 1.90362 | 0.861432 | 0.0590241 | 0.263231 |
0.7 | 55.7315 | 44.5148 | 2.95486 | 1.88855 | 0.840809 | 0.0679255 | 0.304773 |
0.8 | 55.1609 | 45.1194 | 2.94915 | 1.87375 | 0.820834 | 0.076581 | 0.345695 |
0.9 | 54.5995 | 45.7145 | 2.94362 | 1.85922 | 0.801487 | 0.0849982 | 0.386015 |
1. | 54.047 | 46.3003 | 2.93826 | 1.84496 | 0.782748 | 0.0931844 | 0.425749 |
t | Residual error | Residual error | Residual error | Residual error | Residual error | Residual error | Residual error |
|---|---|---|---|---|---|---|---|
0 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
0.1 | \(1.77\times 10^{-15}\) | \(1.77\times 10^{-15}\) | 0. | \(2.77\times 10^{-17}\) | \(3.60\times 10^{-15}\) | \(1.38\times 10^{-17}\) | \(5.55\times 10^{-17}\) |
0.2 | \(1.77\times 10^{-15}\) | \(8.88\times 10^{-16}\) | \(4.16\times 10^{-17}\) | \(5.55\times 10^{-17}\) | \(4.60\times 10^{-13}\) | 0. | \(5.55\times 10^{-17}\) |
0.3 | \(4.97\times 10^{-14}\) | \(4.97\times 10^{-14}\) | \(2.35\times 10^{-16}\) | \(1.66\times 10^{-16}\) | \(7.86\times 10^{-12}\) | \(1.66\times 10^{-16}\) | \(2.22\times 10^{-16}\) |
0.4 | \(6.48\times 10^{-13}\) | \(6.51\times 10^{-13}\) | \(2.76\times 10^{-15}\) | \(2.13\times 10^{-15}\) | \(5.89\times 10^{-11}\) | \(2.27\times 10^{-15}\) | \(3.77\times 10^{-15}\) |
0.5 | \(4.79\times 10^{-12}\) | \(4.82\times 10^{-12}\) | \(2.07\times 10^{-14}\) | \(1.57\times 10^{-14}\) | \(2.80\times 10^{-10}\) | \(1.70\times 10^{-14}\) | \(2.79\times 10^{-14}\) |
0.6 | \(2.46\times 10^{-11}\) | \(2.47\times 10^{-11}\) | \(1.06\times 10^{-13}\) | \(8.12\times 10^{-14}\) | \(1.06\times 10^{-9}\) | \(8.79\times 10^{-14}\) | \(1.44\times 10^{-13}\) |
0.7 | \(9.80\times 10^{-11}\) | \(9.87\times 10^{-11}\) | \(4.28\times 10^{-13}\) | \(3.25\times 10^{-13}\) | \(2.96\times 10^{-9}\) | \(3.51\times 10^{-13}\) | \(5.77\times 10^{-13}\) |
0.8 | \(3.26\times 10^{-10}\) | \(3.26\times 10^{-10}\) | \(1.42\times 10^{-12}\) | \(1.08\times 10^{-12}\) | \(7.54\times 10^{-9}\) | \(1.17\times 10^{-12}\) | \(1.92\times 10^{-12}\) |
0.9 | \(9.38\times 10^{-10}\) | \(9.38\times 10^{-10}\) | \(4.11\times 10^{-12}\) | \(3.12\times 10^{-12}\) | \(1.71\times 10^{-8}\) | \(3.37\times 10^{-12}\) | \(5.54\times 10^{-12}\) |
1 | \(2.39\times 10^{-9}\) | \(2.40\times 10^{-9}\) | \(1.06\times 10^{-11}\) | \(8.06\times 10^{-12}\) | \(3.59\times 10^{-8}\) | \(8.72\times 10^{-12}\) | \(1.43\times 10^{-11}\) |
