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Table 3 Comparison results of the Riccati equation in problem 2 for α=1

From: Fractional-order Riccati differential equation: Analytical approximation and numerical results

t LAPM α = 1 Exact solution Absolute error
y(t) y(t)
1.0 0.7615941560 0.7615941560 0.01235728510 × 10−13
2.0 0.9640275801 0.9640275801 0.00524212251 × 10−12
3.0 0.9950547537 0.9950547537 0.00816114713 × 10−12
4.0 0.9993292997 0.9993292997 1.15746178216 × 10−12
5.0 0.9999092043 0.9999092043 6.17826138530 × 10−11
6.0 0.9999877117 0.9999877117 4.55279023510 × 10−11
7.0 0.9999983377 0.9999983369 7.57246128510 × 10−10
8.0 0.9999997813 0.9999997749 6.33977368904 × 10−9
9.0 1.0000000063 0.9999999695 3.67962922016 × 10−8
10.0 1.0000001574 0.9999999958 1.61485463823 × 10−7
15.0 1.000000000 1.0000000000 0.00002076502676
20.0 1.0000000000 1.0000000000 0.00030117782151
25.0 1.0000000000 1.0000000000 0.00161702848408
30.0 1.0000000000 1.0000000000 0.00510751644687