In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.
Based on the exponential formula of β--decay half-lives for nuclei far from stable line, the half-lives of nuclei around N=82 (R-process waiting point nuclei) are calculated. The results are compared with recent theoretical and experimental data. It is shown that compared with the complicated and time-consuming microscopic calculation, the exponential formula including the shell effect can give the results of β--decay half-lives for R-process waiting point nuclei quicker and better. The results can be used as reliable inputs for the network calculation for nuclei synthesis in cosmos.
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