A Comparison of Fractional and Polynomial Models: Modelling on Number of Subscribers in the Turkish Mobile Telecommunications Market

Önal, Nisa Özge; Karaçuha, Kamil; Karaçuha, Ertuğrul

doi:10.17706/ijapm.2020.10.1.41-48

Cited by 8 publications

(12 citation statements)

References 8 publications

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“…The mathematical model of the GDP per capita of the countries Brazil, China, European Union, India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with our deep assessment method using fractional calculus and compared to the LSTM algorithm which is a deep learning algorithm used for time sequences in general. The result of the proposed method is quite satisfactory and gives better results compared to the other methods including Linear, Polynomial and models which are also compared in [24][25][26] for only modeling. It is considered that better results can be obtained if the model includes other variables such as employment, literacy and population data, etc.…”

Section: Resultsmentioning

confidence: 86%

“…In our previous studies, the children's physical growth, subscriber's numbers of operators, Gross Domestic Product (GDP) per capita were modeled and compared with other modeling approaches such as Linear and Polynomial Models [24][25][26]. According to the results, proposed fractional models had better results compared to the results obtained from Linear and Polynomial Models [24][25][26]. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Karaçuha¹,

Tabatadze²,

Karaçuha³

et al. 2020

Preprint

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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.

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Section: Resultsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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

Karaçuha¹,

Tabatadze²,

Karaçuha³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Here, the fractional derivative is taken with respect to in the order of and (j) corresponds to the ℎ order derivative with respect to . The derivative is generalized by changing the first-order derivative in (6) to fractional derivative in the order of as in (7) [4,8,51,52]. In DAM, is set to 1, and the fractional-order changes between [0,1].…”

Section: A Modeling and Prediction With Deep Assessment Methodologymentioning

confidence: 99%

“…In DAM, is set to 1, and the fractional-order changes between [0,1]. Using the fractional derivative operator which is inserted into the fractional differential equation contributes to the hereditary property [4,8,51,52]. Throughout the paper it is assumed that function ( ) stands for the total number of COVID-19 confirmed cases, recovery from the infection, cumulative deaths over time with the order of is equal to (8).…”

Section: A Modeling and Prediction With Deep Assessment Methodologymentioning

confidence: 99%

Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus

et al. 2020

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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.

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“…In these studies, the children's physical growth, subscriber's numbers of operators, GDP per capita were modeled and compared with other modeling approaches such as Fractional Model-1 and Polynomial Models [34][35][36]. According to the results, proposed fractional models had better results compared to the results obtained from Linear and Polynomial Models [34][35][36]. Our previous works do not take into account the previous values of the dataset for any time instant.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

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.

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A Comparison of Fractional and Polynomial Models: Modelling on Number of Subscribers in the Turkish Mobile Telecommunications Market

Cited by 8 publications

References 8 publications

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

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

Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus

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

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