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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)]