A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the efficiencies of a hybrid solar receiver, which in simple terms is the combination of a photovoltaic system with a thermoelectric system. In addition, a way to reduce the previous system to a nonlinear system of only 2 variables is presented. Naturally, reducing algebraic equation systems of dimension N to systems of smaller dimensions has the main advantage of reducing the number of variables involved in a problem, but the analytical expressions of the systems become more complicated. However, to minimize this disadvantage, an iterative method that does not explicitly depend on the analytical complexity of the system to be solved is used. A fractional iterative method, valid for one and several variables, that uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find solutions of nonlinear systems is presented.

中文翻译：

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使用分数迭代法简化非线性系统及其数值解

对 5 个变量的非线性代数方程系统进行数值求解，该系统源自将傅里叶变换应用于微分方程系统，该微分方程系统允许对混合太阳能接收器的温度行为和效率进行建模，简单来说就是光伏系统与热电系统的组合。此外，还提出了一种将先前系统简化为仅包含 2 个变量的非线性系统的方法。当然，将N维代数方程组简化为更小维数的系统的主要优点是减少问题涉及的变量数量，但系统的解析表达式会变得更加复杂。然而，为了最小化这个缺点，使用了一种不明确依赖于待求解系统的分析复杂性的迭代方法。提出了一种对一个或多个变量有效的分数阶迭代方法，该方法利用分数阶微积分的性质，特别是常数的分数阶导数并不总是为零的事实来寻找非线性系统的解。