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Theory and Modern Applications

Table 1 Illustration of ξ and υ

From: On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum

υ

ξ

 = 510

 = 550

 = 590

 = 610

1.09

0.2038

0.1890

0.1762

0.1650

1.19

0.2430

0.2253

0.2100

0.1967

1.29

0.2883

0.2673

0.2492

0.2333

1.39

0.3405

0.3157

0.2943

0.2756

1.49

0.4006

0.3714

0.3462

0.3242

1.59

0.4693

0.4352

0.4056

0.3799

1.69

0.5479

0.5080

0.4735

0.4434

1.79

0.6373

0.5909

0.5508

0.5158

1.89

0.7389

0.6851

0.6386

0.5981

1.99

0.8540

0.7918

0.7381

0.6912