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Theory and Modern Applications

Table 3 The approximate and exact solutions of \(\pmb{v(x, t)}\) for Example 5.2 for different values of β and \(\pmb{y=0.4}\)

From: New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM

x

t

β  = 0.75

β  = 0.9

β  = 1

Numerical

Exact

0.5

0.3

1.76307

1.58084

1.4918

1.49182

0.6

2.48848

2.17346

2.01296

2.01375

0.9

3.40244

2.95156

2.71191

2.71828

1

0.3

2.90682

2.60637

2.45956

2.4596

0.6

4.10281

3.58343

3.31881

3.32012

0.9

5.60968

4.86629

4.47118

4.48169

1.5

0.3

4.79253

4.29717

4.05514

4.0552

0.6

6.76439

5.90808

5.47179

5.47395

0.9

9.2488

8.02316

7.37174

7.38906