Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data
Natural symmetries exist in several processes of chemistry, physics, and biology. Symmetries possess interesting dynamical characteristics that cannot be seen in non-symmetric systems. The present paper investigates the competition between two banking systems, rural and commercial, in Indonesia, in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/2/542 |
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| author | Mahmoud H. DarAssi Muhammad Altaf Khan Fatmawati Marei Saeed Alqarni |
| author_facet | Mahmoud H. DarAssi Muhammad Altaf Khan Fatmawati Marei Saeed Alqarni |
| author_sort | Mahmoud H. DarAssi |
| collection | DOAJ |
| description | Natural symmetries exist in several processes of chemistry, physics, and biology. Symmetries possess interesting dynamical characteristics that cannot be seen in non-symmetric systems. The present paper investigates the competition between two banking systems, rural and commercial, in Indonesia, in parameterized fractional order Caputo derivative. A novel numerical method is used to discretize the competition system using the real data of rural and commercial banks in Indonesia for the period 2004–2014. The new scheme is more suitable and reliable for data fitting results and has good accuracy. The integer model is formulated in Caputo derivative and their stability results are presented. With the available parameters, the data for the model is analyzed using various scenarios. We shall compare the result with the previous method used in the literature and show that the present method is better than the previous method in the literature. It is shown that fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> involved in the numerical scheme provide excellent fitting. |
| first_indexed | 2024-03-11T08:03:30Z |
| format | Article |
| id | doaj.art-1145f4b06b4241fa944cc77362d404a5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T08:03:30Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1145f4b06b4241fa944cc77362d404a52023-11-16T23:34:41ZengMDPI AGSymmetry2073-89942023-02-0115254210.3390/sym15020542Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real DataMahmoud H. DarAssi0Muhammad Altaf Khan1Fatmawati2Marei Saeed Alqarni3Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, JordanFaculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South AfricaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, IndonesiaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaNatural symmetries exist in several processes of chemistry, physics, and biology. Symmetries possess interesting dynamical characteristics that cannot be seen in non-symmetric systems. The present paper investigates the competition between two banking systems, rural and commercial, in Indonesia, in parameterized fractional order Caputo derivative. A novel numerical method is used to discretize the competition system using the real data of rural and commercial banks in Indonesia for the period 2004–2014. The new scheme is more suitable and reliable for data fitting results and has good accuracy. The integer model is formulated in Caputo derivative and their stability results are presented. With the available parameters, the data for the model is analyzed using various scenarios. We shall compare the result with the previous method used in the literature and show that the present method is better than the previous method in the literature. It is shown that fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> involved in the numerical scheme provide excellent fitting.https://www.mdpi.com/2073-8994/15/2/542parameterized Caputo derivativereal data2004–2014new numerical schemeresults and discussion |
| spellingShingle | Mahmoud H. DarAssi Muhammad Altaf Khan Fatmawati Marei Saeed Alqarni Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data Symmetry parameterized Caputo derivative real data 2004–2014 new numerical scheme results and discussion |
| title | Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data |
| title_full | Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data |
| title_fullStr | Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data |
| title_full_unstemmed | Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data |
| title_short | Analysis of the Competition System Using Parameterized Fractional Differential Equations: Application to Real Data |
| title_sort | analysis of the competition system using parameterized fractional differential equations application to real data |
| topic | parameterized Caputo derivative real data 2004–2014 new numerical scheme results and discussion |
| url | https://www.mdpi.com/2073-8994/15/2/542 |
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