Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method
Many useful numerical algorithms of the numerical solution are proposed due to the increasing interest of the researchers in fractional calculus. A new discretization of the competition model for the real statistical data of banking finance for the years 2004–2014 is presented. We use a novel numeri...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022498?viewType=HTML |
| _version_ | 1828490340018946048 |
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| author | Meihua Huang Pongsakorn Sunthrayuth Amjad Ali Pasha Muhammad Altaf Khan |
| author_facet | Meihua Huang Pongsakorn Sunthrayuth Amjad Ali Pasha Muhammad Altaf Khan |
| author_sort | Meihua Huang |
| collection | DOAJ |
| description | Many useful numerical algorithms of the numerical solution are proposed due to the increasing interest of the researchers in fractional calculus. A new discretization of the competition model for the real statistical data of banking finance for the years 2004–2014 is presented. We use a novel numerical method that is more reliable and accurate which is introduced recently for the solution of ordinary differential equations numerically. We apply this approach to solve our model for the case of Caputo derivative. We apply the Caputo derivative on the competition system and obtain its numerical results. For the numerical solution of the competition model, we use the Newton polynomial approach and present in detail a novel numerical procedure. We utilize the numerical procedure and present various numerical results in the form of graphics. A comparison of the present method versus the predictor corrector method is presented, which shows the same solution behavior to the Newton Polynomial approach. We also suggest that the real data versus model provide good fitting for both the data for the fractional-order parameter value ρ=0.7. Some more values of ρ are used to obtain graphical results. We also check the model in the stochastic version and show the model behaves well when fitting to the data. |
| first_indexed | 2024-12-11T10:41:57Z |
| format | Article |
| id | doaj.art-d31c7e81ecb94f64a6ca4220c4d1036d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T10:41:57Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-d31c7e81ecb94f64a6ca4220c4d1036d2022-12-22T01:10:34ZengAIMS PressAIMS Mathematics2473-69882022-03-01758933895210.3934/math.2022498Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton methodMeihua Huang 0Pongsakorn Sunthrayuth 1Amjad Ali Pasha 2Muhammad Altaf Khan31. School of Marxism Studies (Department of Public Education), Nantong Open University, Nantong, Jiangsu, China2. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, 12110, Thailand3. Aerospace Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia4. Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South AfricaMany useful numerical algorithms of the numerical solution are proposed due to the increasing interest of the researchers in fractional calculus. A new discretization of the competition model for the real statistical data of banking finance for the years 2004–2014 is presented. We use a novel numerical method that is more reliable and accurate which is introduced recently for the solution of ordinary differential equations numerically. We apply this approach to solve our model for the case of Caputo derivative. We apply the Caputo derivative on the competition system and obtain its numerical results. For the numerical solution of the competition model, we use the Newton polynomial approach and present in detail a novel numerical procedure. We utilize the numerical procedure and present various numerical results in the form of graphics. A comparison of the present method versus the predictor corrector method is presented, which shows the same solution behavior to the Newton Polynomial approach. We also suggest that the real data versus model provide good fitting for both the data for the fractional-order parameter value ρ=0.7. Some more values of ρ are used to obtain graphical results. We also check the model in the stochastic version and show the model behaves well when fitting to the data.https://www.aimspress.com/article/doi/10.3934/math.2022498?viewType=HTMLcaputo derivativenewton polynomial approachreal data 2004–2014numerical algorithmstochastic version |
| spellingShingle | Meihua Huang Pongsakorn Sunthrayuth Amjad Ali Pasha Muhammad Altaf Khan Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method AIMS Mathematics caputo derivative newton polynomial approach real data 2004–2014 numerical algorithm stochastic version |
| title | Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method |
| title_full | Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method |
| title_fullStr | Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method |
| title_full_unstemmed | Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method |
| title_short | Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method |
| title_sort | numerical solution of stochastic and fractional competition model in caputo derivative using newton method |
| topic | caputo derivative newton polynomial approach real data 2004–2014 numerical algorithm stochastic version |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022498?viewType=HTML |
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