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Theory and Modern Applications

Table 4 Numerical results of \(\mathcal{S}_{i}\), \(\mathcal{T}_{i}\) and \((\mathcal{S}_{1}+\mathcal{S}_{2})(\widetilde{\vartheta }_{1}+ \widetilde{\vartheta }_{2})+(\mathcal{T}_{1}+\mathcal{T}_{2})( \widehat{\vartheta }_{1}+\widehat{\vartheta }_{2})\) in Example 2

From: Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions

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\(\mathcal{S}_{i}\)

\(\mathcal{T}_{i}\)

\((\mathcal{S}_{1}+\mathcal{S}_{2})(\widetilde{\vartheta }_{1}+\widetilde{\vartheta }_{2}) +(\mathcal{T}_{1}+\mathcal{T}_{2})(\widehat{\vartheta }_{1} + \widehat{\vartheta }_{2})\)

\(\mathcal{S}_{1}\)

\(\mathcal{S}_{2}\)

\(\mathcal{T}_{1}\)

\(\mathcal{T}_{2}\)

1.00

0.0000

0.0000

0.0000

0.0000

0.0000

1.05

0.0015

0.0004

0.0259

0.0044

0.0022

1.10

0.0039

0.0007

0.0344

0.0105

0.0033

1.15

0.0085

0.0010

0.0435

0.0210

0.0048

1.20

0.0151

0.0013

0.0525

0.0352

0.0067

1.25

0.0237

0.0016

0.0615

0.0528

0.0090

1.30

0.0342

0.0019

0.0704

0.0734

0.0115

1.35

0.0466

0.0023

0.0792

0.0968

0.0143

1.40

0.0608

0.0026

0.0879

0.1226

0.0173

1.45

0.0765

0.0030

0.0965

0.1507

0.0205

1.50

0.0937

0.0033

0.1050

0.1807

0.0240

1.55

0.1124

0.0037

0.1134

0.2126

0.0276

1.60

0.1324

0.0041

0.1216

0.2460

0.0314

1.65

0.1535

0.0044

0.1298

0.2810

0.0353

1.70

0.1758

0.0048

0.1379

0.3172

0.0394

1.75

0.1992

0.0052

0.1459

0.3547

0.0436

1.80

0.2235

0.0055

0.1537

0.3932

0.0479

1.85

0.2488

0.0059

0.1615

0.4327

0.0523

1.90

0.2749

0.0063

0.1691

0.4730

0.0568

1.95

0.3017

0.0066

0.1767

0.5142

0.0613

2.00

0.3293

0.0070

0.1841

0.5560

0.0660