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Theory and Modern Applications

Table 1 Numerical results of \(M_{0}\), \(M_{1}\), and ζ in Example 1

From: Using the Hilfer–Katugampola fractional derivative in initial-value Mathieu fractional differential equations with application to a particle in the plane

t

\(M_{0}\)

\(M_{1}\)

ζ

0.00000

−2.4314E − 01

−2.5393E + 01

−9.2100E − 03

0.10472

−2.4314E − 01

−2.5393E + 01

−9.2100E − 03

0.20944

−2.4314E − 01

−2.5393E + 01

−9.2100E − 03

0.31416

−2.4313E − 01

−2.5393E + 01

−9.2100E − 03

0.41888

−2.4312E − 01

−2.5392E + 01

−9.2100E − 03

0.52360

−2.4307E − 01

−2.5386E + 01

−9.2100E − 03

0.62832

−2.4287E − 01

−2.5365E + 01

−9.2100E − 03

0.73304

−2.4227E − 01

−2.5302E + 01

−9.2100E − 03

0.83776

−2.4071E − 01

−2.5139E + 01

−9.2100E − 03

0.94248

−2.3711E − 01

−2.4764E + 01

−9.2000E − 03

1.04720

−2.2955E − 01

−2.3974E + 01

−9.1900E − 03

1.15192

−2.1480E − 01

−2.2433E + 01

−9.1700E − 03

1.25664

−1.8769E − 01

−1.9602E + 01

−9.1100E − 03

1.36136

−1.4032E − 01

−1.4655E + 01

−8.9600E − 03

1.46608

−6.1020E − 02

−6.3734E + 00

−8.2800E − 03

1.57080

6.6950E − 02

6.9923E + 00

−1.1170E − 02

1.67552

2.6702E − 01

2.7888E + 01

−9.9300E − 03

1.78024

5.7122E − 01

5.9658E + 01

−9.7400E − 03

1.88496

1.0225E + 00

1.0679E + 02

−9.6700E − 03

1.98968

1.6775E + 00

1.7520E + 02

−9.6300E − 03

2.09440

2.6098E + 00

2.7257E + 02

−9.6100E − 03

2.19911

3.9136E + 00

4.0874E + 02

−9.6000E − 03

2.30383

5.7082E + 00

5.9616E + 02

−9.5900E − 03

2.40855

8.1425E + 00

8.5040E + 02

−9.5900E − 03

2.51327

1.1401E + 01

1.1908E + 03

−9.5800E − 03

2.61799

1.5712E + 01

1.6409E + 03

−9.5800E − 03

2.72271

2.1349E + 01

2.2296E + 03

−9.5800E − 03

2.82743

2.8646E + 01

2.9917E + 03

−9.5800E − 03

2.93215

3.8001E + 01

3.9689E + 03

−9.5800E − 03

3.03687

4.9891E + 01

5.2106E + 03

−9.5800E − 03