Theory and Modern Applications
Table 2 The consecutive errors of \(K_{\alpha }(2,2)\) for different values \(0<\alpha <1\) at some points
From: Analytic solution of homogeneous time-invariant fractional IVP
(x,y,t) | \(con_{4}(x,t)\) | \(con_{10}(x,t)\) | ||||
|---|---|---|---|---|---|---|
|  | α = 0.25 | α = 0.50 | α = 0.75 | α = 0.25 | α = 0.50 | α = 0.75 |
\(( \frac{\pi }{2},\frac{\pi }{2},0.2 ) \) | 1.2296E−03 | 5.6069E−05 | 1.5026E−06 | 4.4021E−07 | 8.0908E−11 | 4.0523E−15 |
\(( \frac{\pi }{2},\frac{\pi }{2},0.5 ) \) | 3.8655E−03 | 5.5408E−04 | 4.6678E−05 | 5.4701E−06 | 1.2492E−08 | 7.7363E−12 |
\(( \frac{\pi }{2},\frac{\pi }{2},0.8 ) \) | 6.9560E−03 | 1.7942E−03 | 2.7200E−04 | 1.9921E−05 | 1.6570E−07 | 3.7370E−10 |
\(( \pi ,\frac{\pi }{2},0.2 ) \) | 8.6950E−04 | 3.9647E−05 | 1.0625E−06 | 3.1127E−07 | 5.7211E−11 | 2.8588E−15 |
\(( \pi ,\frac{\pi }{2},0.5 ) \) | 2.7333E−03 | 3.9179E−04 | 3.3006E−05 | 3.8679E−06 | 8.8338E−09 | 5.4704E−12 |
\(( \pi ,\frac{\pi }{2},0.8 ) \) | 4.9186E−03 | 1.2687E−03 | 1.9233E−04 | 1.4086E−05 | 1.1716E−07 | 2.6424E−10 |