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Table 4 Comparison between exact solution and approximate solution by using the JF iteration process for \(k=3\) and \(k=11\)

From: Convergence and stability of an iteration process and solution of a fractional differential equation

S. No.

t

k = 3

k = 11

x(t)

\(\tau _{1}\)

\(\tau _{10}\)

x(t)

\(\tau _{1}\)

\(\tau _{10}\)

1

0

0.00000000

0.00000000

0.00000000

0.00000000

0.00000000

0.00000000

2

0.1

0.07127290

0.07127290

0.07127290

0.09420159

0.09420159

0.09420159

3

0.2

0.06081985

0.06081985

0.06081985

0.12109470

0.12109470

0.12109470

4

0.3

0.03349861

0.03349861

0.03349861

0.13856971

0.13856971

0.13856971

5

0.4

−0.00465639

−0.00465639

−0.00465639

0.15014913

0.15014913

0.15014913

6

0.5

−0.05171526

−0.05171526

−0.05171526

0.15632606

0.15632606

0.15632606

7

0.6

−0.10740643

−0.10740643

−0.10740643

0.15643118

0.15643118

0.15643118

8

0.7

−0.17250057

−0.17250057

−0.17250057

0.14894918

0.14894918

0.14894918

9

0.8

−0.24859763

−0.24859763

−0.24859763

0.13146728

0.13146728

0.13146728

10

0.9

−0.33804423

−0.33804423

−0.33804423

0.10046696

0.10046696

0.10046696

11

1.0

−0.44390251

−0.44390251

−0.44390251

0.05101478

0.05101478

0.05101478