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Theory and Modern Applications

Table 2 Numerical comparison between approximate solutions \(u_{\mathrm{ILTM}}\), \(u_{\mathrm{RPSM}}\) and exact solution of (26) for \(y=x=0.5\)

From: Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations

t

γ = 0.8

γ = 1

Absolute error

\(u_{\mathrm{ILTM}}\)

\(u_{\mathrm{RPSM}}\)

\(u_{\mathrm{ILTM}}\)

\(u_{\mathrm{RPSM}}\)

\(|u_{\mathrm{exact}}-u_{\mathrm{ILTM}}|\) for γ = 1

0.01

0.354051

0.333229

0.331345

0.331345

1.54490 × 10−9

0.05

0.357844

0.341156

0.335791

0.335791

1.93035 × 10−7

0.10

0.362610

0.349387

0.341391

0.341391

1.54344 × 10−6

0.15

0.367406

0.356899

0.347038

0.347036

5.20598 × 10−6

0.20

0.372230

0.364004

0.352732

0.352726

1.23320 × 10−5