Theory and Modern Applications
Table 1 Exact and numerical values for \(J=5\), \(c=1\), \(\alpha =1.5\)
From: On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series
x | Exact values of \(\mathfrak{I}_{a,c}^{\alpha }f(x)\) | Numerical values of \(\mathfrak{I}_{a,c}^{\alpha }f(x)\) | Absolute error |
|---|---|---|---|
1.1406 | 0.0068 | 0.008137 | 1.337 × 10−3 |
2.2656 | 0.0711 | 0.072241 | 1.141 × 10−3 |
3.1094 | 0.1190 | 0.119924 | 9.24 × 10−4 |
4.2344 | 0.1681 | 0.168898 | 7.98 × 10−4 |
5.0781 | 0.1956 | 0.196315 | 7.15 × 10−4 |
6.2031 | 0.2232 | 0.223817 | 6.17 × 10−4 |