We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The derivatives considered herein, are taken in Caputo’s sense. The Laplace transform together with the Adomian decomposition method (LADM) is applied to attain analytical approximation of the aforesaid equation. The sG equation having Caputo derivative is solved in the order of series solutions and the results are confirmed by considering two examples with appropriate initial conditions. The numerical simulations are accomplished to compare with the analytical approximations, where qualitatively better agreements are achieved.

中文翻译：

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用拉普拉斯阿多米安分解法研究分数阶正弦-戈登方程

我们分析研究了一个非线性分数阶正弦戈登 (sG) 方程。此处考虑的派生词是在 Caputo 的意义上进行的。应用拉普拉斯变换和阿多米安分解法（LADM）来获得上述方程的解析逼近。具有 Caputo 导数的 sG 方程按级数解的顺序求解，并通过考虑具有适当初始条件的两个示例来确认结果。完成数值模拟以与解析近似值进行比较，从而获得质量上更好的一致性。