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Theory and Modern Applications

Table 9 Comparison of approximate solution and absolute error as \(\alpha =1.0\), \(N= 10\) for solving Example 5 using FAM22, FVIM, and MHPM

From: Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique

t

Exact

FVIM

MHPM

FAM22

Approx.

Error

Approx.

Error

Approx.

Error

0.1

9.9667×10−2

9.9967×10−2

0.0000 ×100

9.9667×10−2

0.0000 ×100

9.9967×10−2

0.0000 ×100

0.2

1.9738×10−1

1.9738×10−1

0.0000 ×100

1.9738×10−1

0.0000 ×100

1.9739×10−1

9.5000×10−5

0.3

2.9131×10−1

2.9132×10−1

8.0000×10−6

2.9131×10−1

0.0000 ×100

2.9133×10−1

1.8121×10−4

0.4

3.7995×10−1

3.8001×10−1

5.7000×10−5

3.7994×10−1

4.0000×10−6

3.7998×10−1

2.5921×10−4

0.5

4.6212×10−1

4.6234×10−1

2.5800×10−4

4.6208×10−1

3.9000×10−5

4.6215×10−1

3.2978×10−4

0.6

5.3705×10−1

5.3792×10−1

8.7400×10−4

5.3686×10−1

1.9200×10−4

5.3709×10−1

3.9363×10−4

0.7

6.0437×10−1

6.0677×10−1

2.4010×10−3

6.0363×10−1

7.3600×10−4

6.0442×10−1

4.5139×10−4

0.8

6.6404×10−1

6.6970×10−1

5.6590×10−3

6.6171×10−1

2.3300×10−3

6.6409×10−1

5.0366×10−4

0.9

7.1630×10−1

7.2814×10−1

1.1842×10−2

7.0992×10−1

6.3780×10−3

7.1685×10−1

5.5094×10−4

1.0

7.6159×10−1

7.8413×10−1

2.2532×10−2

7.4603×10−1

1.5562×10−2

7.6218×10−1

5.9372×10−4