The RL and RC circuits are analyzed in this research paper. The classical model of these circuits is generalized using the modern concept of fractional derivative with Mittag-Leffler function in its kernel. The fractional differential equations are solved for exact solutions using the Laplace transform technique and the inverse transformation. The obtained solutions are plotted and presented in tables to show the effect of resistance, inductance and fractional parameter on current and voltage. Furthermore, the statistical analysis is presented to predict the seasonal of time and other parameters on the current flowing in the circuit. The statistical analysis shows that the variation in current is insignificant with respect to time and is more significant with respect to other parameters.

中文翻译：

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RL和RC分数阶电路的数学和统计分析

本研究论文分析了 RL 和 RC 电路。这些电路的经典模型使用现代分数导数概念进行了概括，其内核具有 Mittag-Leffler 函数。使用拉普拉斯变换技术和逆变换求解分数微分方程以获得精确解。将获得的解决方案绘制并以表格形式呈现，以显示电阻、电感和分数参数对电流和电压的影响。此外，还提出了统计分析来预测电路中流动的电流的时间和其他参数的季节性。统计分析表明，电流的变化相对于时间不显着，相对于其他参数更显着。