Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 24 February 2020 / Approved: 25 February 2020 / Online: 25 February 2020 (11:16:07 CET)

A peer-reviewed article of this Preprint also exists.

Karaçuha, E.; Tabatadze, V.; Karaçuha, K.; Önal, N.Ö.; Ergün, E. Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries. Mathematics 2020, 8, 633. Karaçuha, E.; Tabatadze, V.; Karaçuha, K.; Önal, N.Ö.; Ergün, E. Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries. Mathematics 2020, 8, 633.

## Abstract

In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

## Keywords

deep assessment; fractional calculus; least squares; modeling; GDP per capita; prediction

## Subject

Computer Science and Mathematics, Applied Mathematics