Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Population of Countries

Abstract

The modelling of data and prediction for the upcoming years or events are one of the main concerns of not only all countries but also companies, investors, manufacturers, and institutions. The scientists investigate on a relation among telecommunication, economic growth, and financial development using technical, economic, social events and data. Besides, the population changes affect balances in any aspect. Therefore, the prediction of the population for each country is prominent and essential for the other prediction. In this study, the dataset consists of the populations of the USA, France, Britain, Italy, Spain, and Turkey were used from 1960 until 2018. In our study, populations of countries are tried to be modelled, and the predictions are made for the upcoming years, using fractional calculus. The newly developed approach uses the data for the modelling by employing Least Squares method and fractional calculus.

Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries

“…Note that, unknown model coefficients in (2.7b) are optimized for the test prediction (2018) with minimum error. For instance, in our previous study [4], modeling error of Italy, Spain, Turkey and UK are obtained as 0.12%, 0.52%, 0.15% and 0.19% respectively for early Deep Assessment model on population data. The Fifth and sixth columns illustrate Deep Assessment and Deep Learning prediction errors for = 58.…”

“…Developments in technology and informatics parallel with data science lead the companies, institutions, universities and especially, the countries to give priority to evaluating produced data and predicting what can be forthcoming. The modeling of all technical, economic, social events and data has been the interest of scientists for many years [1][2][3][4]. There are many authors investigating on the modeling and predicting events, options, choices and data.…”

“…Different from the previous research, the study works not only for modeling as it is done previously, but also for the prediction of next coming values. Here, the modeling is implemented with the similar mathematical tools developed in the previous study [4] with a different approach in which the finite numbers of previous values and the derivatives are taken into account. Then, the prediction is obtained by dividing the dataset into four regions which will be explained in the following section.…”

Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries

“…Developments in technology and informatics in parallel with the development of data science lead the companies, institutions, universities and especially, the countries to give priority to evaluating produced data and predicting what can be forthcoming. The modeling of all technical, economic, social events and data has been the interest of scientists for many years [1][2][3][4]. Many authors have been investigating the modeling and predicting events, options, choices and data.…”

“…The proposed approach is built on the fractional-order differential equation and corresponding Laplace transform properties are utilized. Here, the modeling is implemented with mathematical tools similar to those developed in the previous study [4] with a different approach in which the finite numbers of previous values and the derivatives are taken into account. Then, the prediction is obtained by assuming a value in a specific time can be expressed as the summation of the previous values weighted by unknown coefficients and the function to be modeled is continuous and differentiable.…”