This paper presents a method for predicting the energy yield of a photovoltaic (PV) system based on the ARIMA algorithm. We analyze two key time series: the specific yield and the total yield of the PV system. Two ARIMA models are developed for each time series: one selected by the authors and one determined by SPSS. Model performance is evaluated through fit statistics, providing a comprehensive assessment of model accuracy. The residuals’ ACF and PACF are examined to ensure model adequacy, and confidence intervals are calculated for residuals to validate the models. A monthly forecast is then generated for both time series, complete with confidence intervals, to demonstrate the models’ predictive capabilities. The results highlight the effectiveness of ARIMA in forecasting PV energy yields, offering valuable insights for optimizing PV system performance and planning. This study contributes to the field of renewable energy forecasting by demonstrating the applicability of ARIMA models in predicting the monthly performance of photovoltaic systems.

In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function. We prove the convergence of the approximation and derive an estimate for the error and order. The approximation is applied for the construction of finite difference schemes for the two-term ordinary fractional differential equation and the time fractional Black–Scholes equation for option pricing. The properties of the approximation are used to prove the convergence and order of the finite difference schemes and to obtain bounds for the error of the numerical methods. The theoretical results for the order and error of the methods are illustrated by the results of the numerical experiments.

Artificial intelligence could be used as a powerful and innovative tool in mathematics education. It is poised to transform the way of learning and teaching this subject.The main objective of our study is to provide a more complete and thorough understanding of the role and impact of using AI in mathematics education by determining the trends, the AI methods, the technological applications and the opportunities for utilizing AI by teachers and students. The potential benefits and threats caused by the use of AI are also discussed.

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed.