In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter . Three illustrative examples were included to show the effectiveness and importance of the proposed techniques.

中文翻译：

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从优化问题中求解基于非线性分数阶梯度的动态系统的最优同伦渐近方法-最小二乘

在本文中，我们考虑了一种最佳同伦渐近方法-最小二乘（OHAM-LS）的近似分析方法，以获得由非线性规划（NLP）优化问题产生的基于非线性分数阶梯度的动态系统（FOGBDS）的解决方案。该问题由一类非线性分数阶微分方程（FDE）公式化，并用最速下降法的适形分数阶导数（CFD）建模该方程的解，以找到问题的最小化点。该公式将优化问题的整数解扩展为任意阶解。我们展示了OHAM-LS使我们能够确定通过启动收敛控制参数而获得的级数解的收敛域。 包括三个说明性示例，以显示所提出技术的有效性和重要性。