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Figure 1 | Advances in Difference Equations

Figure 1

From: Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets

Figure 1

(a) Numerical simulation of Eq. (50) for \(\alpha =1\), (b) 3D surface solution for \(\alpha =\frac{1}{2}\), (c) 3D non-differentiable surface solution behavior for \(\alpha =\frac{\ln (2)}{\ln (3)}\), (d) 2D approximate solutions for \(\alpha =1,\frac{1}{2}\) and \(\frac{\ln (2)}{\ln (3)}\), (e) Absolute error \(E_{10}(v(x,t))=|v_{\mathrm{ext}.}(x,t)-v_{\mathrm{appr}.}(x,t)|\) for \(\alpha =1\), (f) Absolute error \(E_{20}(v(x,t))=|v_{\mathrm{ext}.}(x,t)-v_{\mathrm{appr}.}(x,t)|\), \(\alpha =1\), (g) Absolute error of the LFHAM \(E_{10}(v(x,t))=|v_{\mathrm{ext}.}(x,t)-v_{\mathrm{appr}.}(x,t)|\) when \(\alpha =\frac{\ln (2)}{\ln (3)}\), (h) Absolute error of the LFHAM \(E_{20}(v(x,t))=|v_{\mathrm{ext}.}(x,t)-v_{\mathrm{appr}.}(x,t)|\) when \(\alpha =\frac{\ln (2)}{\ln (3)}\)

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