UNAIR NEWS – Faculty of Science and Technology (FST) Mathematics lecturer of Universitas Airlangga, Dr. Fatmawati, MSi. in a team, recently has conducted a study on the differences between commercial banks and rural banks (BPR). Interestingly, she used mathematical models in doing it.
The fractional model is used as a research model. The fractional model used three fractional derivatives, Caputo, Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). From the results of her research simulation, she proved that the results of AB fractional derivative is more accurate and flexible in modeling competition between commercial banks and rural banks in Indonesia.
“There are more rural banks than commercial banks because commercial banks have more activities while rural banks have fewer business activities,” she said.
Fatmawati revealed that rural banks’ business activities are less as they only collected funds from the public for term deposits, credit, and placed funds in the form of Bank Indonesia Certificates. They are not allowed to accept funds in the form of deposits in the form of demand deposits, participate in payment traffic, conduct business activities in foreign currencies, carry out equity participation and conduct insurance business.
Fatmawati also said that in AB analysis, BPR has a smaller profit compared to commercial banks and can improve their products and activities. She also revealed that the products of the two types of banks did not have many differences and there might be competition to get customers to make a profit.
Fatmawati also explained the existence of competition between rural banks and commercial banks in Indonesia. The dynamic competition of these two types of banks can be described through Lotka-Volterra type competition model introduced by Alfred J. Lotka and Vito Volterra in 1920.
According to her, this model consists of two equations that describe the competition of two species for food. The Lotka-Volterra type model has been widely used to describe the dynamic competition of telecommunications companies in Korea and also Korean stock market with the classical differential equation system approach.
The fractional integral model used by Fatmawati has become an important concept in the study of fractional calculus. The model has been used as a useful tool in modeling complex problems that cannot be accommodated by models with classical integer derivatives. One of the advantages is that it can describe the effect of memory and in some real cases can provide results that are suitable both in banking cases. (*)
Author: Aditya Novrian
Editor: Nuri Hermawan
Wanting Wang, Muhammad Altaf Khan, Fatmawati , P. Kumam, P. Thounthong. 2019. A comparison study of bank data in fractional calculus. Elsevier Ltd, Chaos, Solitons and Fractals, Volume 126 (2019), 369–384