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The two approaches to solving nonlinear Caputo time-fractional wave-like equations with variable coefficients are examined in this study. The Homotopy perturbation transform method and the Yang transform decomposition method are the names of these two techniques. Three separate numerical examples are provided to demonstrate the effectiveness and pr...
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... graphs in Figures 1(a) and 1(b) show the behavior of the exact and proposed methods solution in Caputo manner at ℘ = 1. Figure 1(c) shows our methods solution at different fractional-orders of ℘ = 2, 1.9, 1.8, 1.7, and −1 ≤ y, z ≤ 1 for Example 1 and Figure 1(d), respectively, at ς = 0.1 and −1 ≤ y, z ≤ 1. In Table 1, we computed the absolute errors of the Shehu variational iteration method (SVIM) and suggested methods that confirm that our solution converges quickly compared to SVIM. ...
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... graphs in Figures 1(a) and 1(b) show the behavior of the exact and proposed methods solution in Caputo manner at ℘ = 1. Figure 1(c) shows our methods solution at different fractional-orders of ℘ = 2, 1.9, 1.8, 1.7, and −1 ≤ y, z ≤ 1 for Example 1 and Figure 1(d), respectively, at ς = 0.1 and −1 ≤ y, z ≤ 1. In Table 1, we computed the absolute errors of the Shehu variational iteration method (SVIM) and suggested methods that confirm that our solution converges quickly compared to SVIM. ...
Context 3
... graphs in Figures 1(a) and 1(b) show the behavior of the exact and proposed methods solution in Caputo manner at ℘ = 1. Figure 1(c) shows our methods solution at different fractional-orders of ℘ = 2, 1.9, 1.8, 1.7, and −1 ≤ y, z ≤ 1 for Example 1 and Figure 1(d), respectively, at ς = 0.1 and −1 ≤ y, z ≤ 1. In Table 1, we computed the absolute errors of the Shehu variational iteration method (SVIM) and suggested methods that confirm that our solution converges quickly compared to SVIM. ...
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Citations
... Alshehry et al [28] described a numerical solution of a non-linear system of fractional PDEs by applying Yang transform in addition with the Residual Power technique. Some of the updated work in this regard is as follows [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. ...
A novel approach to locate the approximate analytical solutions for non-linear partial differential equations is presented in this paper: the Yang transformation method combined with the Caputo derivative. In the current work, we determine the fractional Heat and Wave equation’s approximate analytical solutions. This current work addresses the Yang transformation approach in addition with the Caputo derivative. The suggested method yields approximately analytical solutions in the form of series with a simple, straightforward mechanics and a proportionality dependent on values of the fractional-order derivative. A few numerical heat equation and wave equation problems are solved to show the usefulness and reliability of the method. The tabular form [tables 7–12] makes the claim that the absolute error decreased as the number of terms in the series increased. It is also confirmed that the results are graphical compatible.
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