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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 5 Differential transforms $G_{i} (k)$ for $g (t) = y (t) ln [y (t)]$ , $k = 0, 1, 2, 3, 4$

k	$G_{i} (k)$
0	$Y_{i} (0) ln [Y_{i} (0)]$
1	$Y_{i} (1) ln [Y_{i} (0)] + Y_{i} (1)$
2	$Y_{i} (2) ln [Y_{i} (0)] + Y_{i} (2) + \frac{{(Y_{i} (1))}^{2}}{2 Y_{i} (0)}$
3	$Y_{i} (3) ln [Y_{i} (0)] + Y_{i} (3) + \frac{Y_{i} (1) Y_{i} (2)}{Y_{i} (0)} - \frac{{(Y_{i} (1))}^{3}}{6 {(Y_{i} (0))}^{2}}$
4	$Y_{i} (4) ln [Y_{i} (0)] + Y_{i} (4) + \frac{2 Y_{i} (1) Y_{i} (3) + {(Y_{i} (2))}^{2}}{2 Y_{i} (0)} - \frac{{(Y_{i} (0))}^{2} Y_{i} (2)}{2 {(Y_{i} (0))}^{2}} + \frac{{(Y_{i} (1))}^{4}}{12 {(Y_{i} (0))}^{3}}$