Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Differential transforms $G_{i} (k)$ for $g (t) = exp [y (t)]$ , $k = 0, 1, 2, 3, 4$

From: A semi-analytic method with an effect of memory for solving fractional differential equations

k	$G_{i} (k)$
0	$exp [Y_{i} (0)]$
1	$Y_{i} (1) exp [Y_{i} (0)]$
2	$({(Y_{i} (1))}^{2} / 2 + Y_{i} (2)) exp [Y_{i} (0)]$
3	$({(Y_{i} (1))}^{3} / 3! + Y_{i} (1) Y_{i} (2) + Y_{i} (3)) exp [Y_{i} (0)]$
4	$({(Y_{i} (1))}^{4} / 4! + {(Y_{i} (1))}^{2} Y_{i} (2) / 2! + {(Y_{i} (2))}^{2} / 2 + Y_{i} (1) Y_{i} (3) + Y_{i} (4)) exp [Y_{i} (0)]$

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