In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

中文翻译：

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迭代方法应用于由 MITTAG-LEFFLE 内核产生的热弹性的分数非线性系统

在本文中，我们研究了代表热弹性中出现的一维柯西问题的分数非线性方程组的数值解。所提出的技术是拉普拉斯变换技术与[公式：见正文]-同伦分析方案和用 Atangana-Baleanu (AB) 算子定义的分数导数的优雅融合。为了证明所提出的分数阶模型所获得解的存在性和唯一性，考虑了不动点假设。为了说明和验证未来技术的效率，我们考虑了三种不同的情况，并根据分数阶分析了投影模型。此外，所获得解决方案的物理行为已根据不同分数阶的图进行捕获，并通过数值模拟来保证准确性。所得结果表明，该方案易于实现，系统性强，可准确分析科学与工程相关领域中出现的任意阶耦合非线性微分方程的行为。