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.

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This work focuses on the influence of a simple pole on a new function representing method we called separate node ascending derivatives expansion (SNADE) convergence characteristics. Even though SNADE can be somehow considered as a new Taylor series expansion, it is distincted from Taylor series expansion by its different nodal points using features. This paper focuses on certain details of SNADE about convergence and its validity. Beyond that, this research focusing on the influence of a simple pole location in the function on the convergence characteristics involves completely new original findings and reported in this paper where a specific importance is given to the case where the SNADE nodal sequence is composed of elements alternating between two nodal values.

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Infinite dimensional quantum information geometry AIP Conf.Abstract. This preliminary work aims at the formulation of the perturbative recursions for the HDMR component determination when the weight function is nonproduct type. The deviations from the product type, and, related items are used as the perturbing agents. By introducing a perturbation parameter to these terms serve us to expand the unknowns in powers of the perturbation parameter. Only the recursive equations are constructed here. The true implementations and algorithm construction has been left to future works.