This study focuses on modeling, prediction, and analysis of confirmed, recovered, and death cases of COVID-19 by using Fractional Calculus in comparison with other models for 8 countries including China, France, Italy, Spain, Turkey, the UK, and the US. First, the dataset is modeled using our previously proposed approach Deep Assessment Methodology, next, one step prediction of the future is made using two methods: Deep Assessment Methodology and Long Short-Term Memory. Later, a Gaussian prediction model is proposed to predict the short-term (30 Days) future of the pandemic, and prediction performance is evaluated. The proposed Gaussian model is compared to a time-dependent susceptible-infected-recovered (SIR) model. Lastly, an analysis of understanding the effect of history is made on memory vectors using wavelet-based denoising and correlation coefficients. Results prove that Deep Assessment Methodology successfully models the dataset with 0.6671%, 0.6957%, and 0.5756% average errors for confirmed, recovered, and death cases, respectively. We found that using the proposed Gaussian approach underestimates the trend of the pandemic and the fastest increase is observed in the US while the slowest is observed in China and Spain. Analysis of the past showed that, for all countries except Turkey, the current time instant is mainly dependent on the past two weeks where countries like Germany, Italy, and the UK have a shorter average incubation period when compared to the US and France.

In this study, a new approach for time series modeling and prediction, “deep assessment methodology,” is proposed and the performance is reported on modeling and prediction for upcoming years of Gross Domestic Product (GDP) per capita. The proposed methodology expresses a function with the finite summation of its previous values and derivatives combining fractional calculus and the Least Square Method to find unknown coefficients. The dataset of GDP per capita used in this study includes nine countries (Brazil, China, India, Italy, Japan, the UK, the USA, Spain and Turkey) and the European Union. The modeling performance of the proposed model is compared with the Polynomial model and the Fractional model and prediction performance is compared to a special type of neural network, Long Short-Term Memory (LSTM), that used for time series. Results show that using Deep Assessment Methodology yields promising modeling and prediction results for GDP per capita. The proposed method is outperforming Polynomial model and Fractional model by 1.538% and by 1.899% average error rates, respectively. We also show that Deep Assessment Method (DAM) is superior to plain LSTM on prediction for upcoming GDP per capita values by 1.21% average error.

In this article, the plane wave diffraction by two strips is studied. Fractional boundary condition is required on strips when the fractional order for each strip is different. The goal of the paper is to investigate the resonant properties of such structures. The mathematical apparatus for the solution of the problem is given. The frequency dependency on the total radar cross-section is constructed for the different combinations of the fractional order. At the resonant frequencies, the near and the far-field distributions are presented.

In this article, the diffraction of the electromagnetic wave by the building with two rooms is considered. The rooms have doors and windows with lossy dielectric walls. The electromagnetic properties of the building as an opened coupled resonator system are investigated at different source locations and several frequencies including 5G band. The problem is solved by using the Method of Auxiliary Sources. The near electric field distributions are calculated and analyzed.