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Table 5 Numerical results of \(\int _{0}^{\mathfrak{s}} \frac{ ( \mathfrak{s} - q\grave{\iota} )^{ ( \nu -1 ) }}{\Gamma _{q} ( \nu ) } \upphi (\grave{\iota}) \, {\mathrm {d}}_{q}\grave{\iota} \) for \(q \in \{\frac{1}{7}, \frac{1}{2}, \frac{8}{9} \} \) in Example 5.1

From: Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

\(\mathfrak{s}\)

\(q=\frac{1}{7}\)

\(q=\frac{1}{2}\)

\(q=\frac{8}{9}\)

0.00

0.00000

0.00000

0.00000

0.10

0.00141

0.00102

0.00074

0.20

0.00978

0.00711

0.00513

0.30

0.03045

0.02211

0.01595

0.40

0.06814

0.04949

0.03570

0.50

0.12727

0.09243

0.06668

0.60

0.21205

0.15401

0.11109

0.70

0.32650

0.23713

0.17106

0.80

0.47453

0.34464

0.24861

0.90

0.65992

0.47928

0.34574

1.00