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.

翻译：本文对一个五变量非线性代数方程组进行了数值求解，该方程组源自对微分方程组应用傅里叶变换，该微分方程组可用于模拟混合太阳能接收器的温度分布与效率特性。简而言之，该接收器是光伏系统与热电系统的结合体。此外，本文提出了一种将原系统降维为仅含两个变量的非线性系统的方法。自然而言，将N维代数方程组降维至更低维度的主要优势在于减少问题所涉及的变量数目，但系统的解析表达式会随之变得更为复杂。为降低此不利影响，本文采用了一种迭代方法，其不显式依赖于待求解系统的解析复杂度。文中提出了一种适用于单变量及多变量情形的分数阶迭代法，该方法利用分数阶微积分的特性（特别是分数阶导数对常数的求导结果不一定为零这一性质）来求解非线性系统。