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Theory and Modern Applications

Table 1 The consecutive errors of \(K_{\alpha }(2,2)\) for different values \(0<\alpha <1\) at some points

From: Analytic solution of homogeneous time-invariant fractional IVP

(x,t)

\(con_{4}(x,t)\)

\(con_{10}(x,t)\)

 

α = 0.25

α = 0.50

α = 0.75

α = 0.25

α = 0.50

α = 0.75

\(( \frac{\pi }{2},0.2 ) \)

1.7390E−03

7.9294E−05

2.1250E−06

6.2255E−07

1.1442E−10

5.7731E−15

\(( \frac{\pi }{2},0.5 ) \)

5.4667E−03

7.8359E−04

6.6013E−05

7.7359E−06

1.7667E−08

1.0940E−11

\(( \frac{\pi }{2},0.8 ) \)

9.8372E−03

2.5374E−03

3.8466E−04

2.8173E−05

2.3433E−07

5.2849E−10

(Ï€,0.2)

2.4593E−03

1.1213E−04

3.0052E−06

8.8043E−07

1.6181E−10

8.1046E−15

(Ï€,0.5)

7.7310E−03

1.1081E−03

9.3357E−05

1.0940E−05

2.4985E−08

1.5472E−11

(Ï€,0.8)

1.3912E−02

3.5884E−03

5.4400E−04

3.9843E−05

3.3140E−07

7.4740E−10