In this paper, we find the solution and analyse the behaviour of the obtained results for the nonlinear Schrödinger‐Boussinesq equations using q‐homotopy analysis transform method (q‐HATM) within the frame of fractional order. The considered system describes the interfaces between intermediate long and short waves. The projected fractional operator is proposed with the help of Mittag‐Leffler function to incorporate the nonsingular kernel to the system. The projected algorithm is a modified and accurate method with the help of Laplace transform. The convergence analysis is presented with the help of the fixed point theorem in the form existence and uniqueness. To validate and illustrate the effectiveness of the algorithm considered, we exemplified considered system with respect of arbitrary order. Further, the behaviour of achieved results is captured in contour and 3D plots for distinct arbitrary order. The results show that the projected scheme is very effective, highly methodical and easy to apply for complex and nonlinear systems and help us to captured associated behaviour diverse classes of the phenomenon.

中文翻译：

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具有Mittag-Leffler核的分数阶Schrödinger-Boussinesq方程的新方法

在本文中，我们找到了解决方案，并使用q同伦分析变换方法（q将对非线性Schrödinger-Boussinesq方程的结果进行了分析-HATM）。所考虑的系统描述了中间长波和短波之间的界面。借助Mittag-Leffler函数提出了投影分数算子，以将非奇异内核合并到系统中。该投影算法是在拉普拉斯变换的帮助下改进而精确的方法。在不动点定理的帮助下，以存在性和唯一性的形式给出收敛性分析。为了验证和说明所考虑算法的有效性，我们以任意顺序为例对所考虑系统进行了示例。此外，在轮廓图和3D图中以截然不同的任意顺序捕获了所获得结果的行为。结果表明，该方案是非常有效的，