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Table 3 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 6.2 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

1.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1.1052

0.0602

0.1059

0.0307

0.0384

0.0119

0.0001

1.2214

0.1299

0.2284

0.0662

0.0771

0.0793

0.0063

1.3499

0.2091

0.3677

0.1065

0.1157

0.2572

0.0661

1.4918

0.2975

0.4325

0.1253

0.1539

0.6196

0.3839

1.6487

0.3942

0.4325

0.1253

0.1913

1.2649

1.5999

1.8221

0.4975

0.4325

0.1253

0.2273

2.3154

5.3612

2.0138

0.6046

0.4325

0.1253

0.2610

3.9084

15.2758

2.2255

0.7105

0.4325

0.1253

0.2913

6.1656

38.0151

2.4596

0.8056

0.4325

0.1253

0.3162

9.1216

83.2040

2.7183

0.8654

0.4325

0.1253

0.3307

12.5716

158.0444