Table 10 The comparison of error norms with \(\sigma\) = 0.5, \(M\) = 80, \(\Delta t\) = 0.00025, and \(\hat{\nu }\) = 1 at \(t\) = 1 for various values of fractional order \(\alpha\) for Example 2

Present

\(L_{2}\)

1.8876e−05

1.6380e−05

1.3566e−06

4.1799e−07

\(L_{\infty }\)

2.6330e−05

2.2826e−05

1.9250e−06

5.9768e−07

Ref. [19]

\(L_{2}\)

3.492e−06

2.733e−06

1.520e−06

1.886e−06

\(L_{\infty }\)

6.455e−06

5.257e−06

3.443e−06

4.065e−06

Ref. [35]

\(L_{2}\)

1.0027e−05

9.121e−06

2.297e−06

5.283e−06

\(L_{\infty }\)

2.2129e−05

2.0782e−05

8.187e−06

7.886e−06