This study explores the modeling of the share of telecommunication revenues in gross domestic product from the year 2000 to 2018 for 5 countries including France, Germany, Italy, Turkey, the UK, and the OECD average. First, a new mathematical model based on Fractional Calculus and Least Square Method is proposed. Later, the telecommunication revenues in GDP dataset is modeled. Further, we compare the new Fractional approach to the classical Polynomial approach in three different settings. The results show that employing Fractional Calculus yields better modeling performance when compared to the classical Polynomial Approach in terms of Mean Absolute Percentage Error (MAPE). The Fractional approach outperforms the Polynomial approach by 0.1329 % MAPE on average. The largest MAPE is found for Turkey while the smallest MAPE is obtained for Italy in all settings.

Today, operators have become the resource of telecommunications data. Therefore, knowledge about subscriptions is easily available for most countries. In recent years, high-speed mobile internet access subscriptions are also increasing rapidly. There are two important subscriptions reviewed by The International Telecommunication Union (ITU): mobile broadband (MBB) subscriptions and Fixed broadband (FBB) subscriptions. In this study, we proposed an original mathematical model employing the fractional analysis theory and evaluate its validity by modeling the mobile broadband and fixed broadband subscriptions of six countries including France, Italy, Turkey, Germany, Spain, and the U.K. Later, we compared the Fractional Model we developed with the Polynomial Model. The results show that the Fractional Model is superior to the conventional Polynomial Model in modeling broadband subscriptions. For all selected countries, our proposed Fractional approach outperforms conventional polynomial regression. For all investigation categories, on average, the fractional approach works better by at least 10% and at most 30%.

This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample flights, we propose a novel approach combining deep assessment methodology (DAM) with fractional calculus theory. By modeling the relationship between PLF and the number of days remaining until a flight, our method yields minimal errors compared to traditional techniques. Through a continuous curve constructed using the least-squares approach, we enable the anticipation of future flight values. Our analysis demonstrates that the DAM model with a first-order derivative outperforms linear techniques and the Fractional Model-3 in both modeling capabilities and prediction accuracy. The proposed approach offers a data-driven solution for efficiently managing air transport capacity, with implications for revenue optimization. Specifically, our modeling findings indicate that the DAM wd model improves prediction accuracy by approximately 0.67 times compared to the DAM model, surpassing the fractional model and regression analysis. For the DAM wd modeling method, the lowest average mean absolute percentage error (AMAPE) value achieved is 0.571, showcasing its effectiveness in forecasting flight outcomes.

Aviation is one of the most global industries, and if we can model and predict a country’s air transportation flow and indicators ahead of time, we may be able to use it as a key decision-making tool for the management and operation process. This study proposes a new modeling, and prediction method that employs both fractional calculus and Multi Deep Assessment Methodology (MDAM) techniques. For the application, air passengers carried, air freight, available seat kilometers, number of flights, destination points, international travelers, international destination points, and international flight data between 2011 and 2019 for eight countries with the busiest airports were chosen. As a result, the highest modeling error was discovered to be Germany’s air transport freight factor expressed as a percentage of 1,59E-02. The percentage of predictions with errors less than 10% was 90.278. We also compared the performance of two different MDAM methodologies. The novel MDAM wd methodology proposed in this paper has a higher accuracy in aviation factors prediction and modeling.