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Table 1 Numerical values of \(\int ^{ \grave{ \iota}}_{\grave{a}} \mathcal{G}_{1} (\grave{\iota}, \xi ) \,{\mathrm {d}}\xi \), \(\breve{M}_{2}\), γ, \(\int _{\grave{a}}^{\grave{\iota}} \mathcal{G}_{2}(\grave{\iota}, \xi ) \,{\mathrm {d}}\xi \), \(\int _{\grave{a}}^{\grave{\iota}} \mathcal{H}(\grave{a}, \xi ) \hslash (\xi ) \,{\mathrm {d}}\xi \), and \(\Delta =\upphi _{\bar{p}} ( \int _{\grave{a}}^{\grave{\iota}} \mathcal{H}(\grave{a}, \xi ) \hslash (\xi ) \,{\mathrm {d}}\xi )\) in Example 6.1 for \(\tau \in J\)

From: Existence of positive solutions for p-Laplacian boundary value problems of fractional differential equations

τ

\(\int ^{\tau}_{\grave{a}} \mathcal{G}_{1} (\grave{\iota}, \xi ) \,{\mathrm {d}}\xi \)

\(\breve{M}_{2}\)

γ

\(\int _{\grave{a}}^{\tau} \mathcal{G}_{2}(\grave{\iota}, \xi ) \,{\mathrm {d}}\xi \)

\(\int _{\grave{a}}^{\tau} \mathcal{H}(\grave{a}, \xi ) \hslash (\xi ) \,{\mathrm {d}}\xi \)

Δ

2.7183

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

3.0377

0.2357

0.0039

0.0011

0.3462

3.7320

13.9275

3.3947

0.5121

0.0085

0.0025

0.6944

10.0873

101.7541

3.7937

0.8293

0.0138

0.0040

1.0416

18.4145

339.0940

4.2395

1.1850

0.0197

0.0057

1.3835

28.8166

830.3948

4.7377

1.5738

0.0261

0.0076

1.7148

41.5311

1724.8351

5.2945

1.9852

0.0329

0.0095

2.0276

56.8307

3229.7341

5.9167

2.3994

0.0398

0.0115

2.3105

74.9520

5617.7976

6.6120

2.7785

0.0461

0.0133

2.5445

95.9883

9213.7513

7.3891

3.0207

0.0501

0.0145

2.6809

119.6935

14,326.5251