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Theory and Modern Applications

Table 2 Numerical results of the Riccati equation in problem 1 for α=1, 1 2 , 3 4

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

t

α= 1 2 GEM

α= 1 2 LAPM

α= 3 4 GEM

α= 3 4 LAPM

α = 1 LAPM

0.1

0.3568251903

0.3568031433

0.1934884034

0.1934012434

0.1102952044

0.2

0.9228652311

0.9228654512

0.4546091238

0.4546025138

0.2419783394

0.3

1.6341391963

1.6341391234

0.7840321022

0.7840324522

0.3951442714

0.4

2.2044414876

2.2044414576

1.1619801122

1.1619856232

0.5682377001

0.5

2.4004512311

2.4004476111

1.5438814841

1.5438814521

0.7588607194

0.6

2.0414276521

2.0414345521

1.8736212813

1.873658343

0.8840411201

0.7

2.4142176521

2.414888821

2.1129313512

2.112943562

1.0827124311

0.8

2.4142456641

2.4142478941

2.2602500123

2.260134223

1.2820124311

0.9

2.4142456047

2.4142455667

2.339920199

2.339134229

1.4740612089

1

2.4142410607

2.4142312137

2.3795146712

2.37935612

1. 6515902374