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

Advances in Difference Equations

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	$Y i (2) ln [Y i (0)] + Y i (2) + (Y i (1)) 2 2 Y i (0)$
3	$Y i (3) ln [Y i (0)] + Y i (3) + Y i (1) Y i (2) Y i (0) − (Y i (1)) 3 6 (Y i (0)) 2$
4	$Y i (4) ln [Y i (0)] + Y i (4) + 2 Y i (1) Y i (3) + (Y i (2)) 2 2 Y i (0) − (Y i (0)) 2 Y i (2) 2 (Y i (0)) 2 + (Y i (1)) 4 12 (Y i (0)) 3$