A numerical scheme for fractional order mortgage model of economics
In this article, the famous mortgage model of economics is investigated by developing a numerical scheme. The considered model is proposed under the Caputo power law derivative of fractional order. Further, in the considered model by utilizing the time esteem of cash rule, we build up break even wit...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-05-01
|
| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000134 |
| _version_ | 1797815485219209216 |
|---|---|
| author | Hafsa Naz Thongchai Dumrongpokaphan Thanin Sitthiwirattham Hussam Alrabaiah Khursheed J. Ansari |
| author_facet | Hafsa Naz Thongchai Dumrongpokaphan Thanin Sitthiwirattham Hussam Alrabaiah Khursheed J. Ansari |
| author_sort | Hafsa Naz |
| collection | DOAJ |
| description | In this article, the famous mortgage model of economics is investigated by developing a numerical scheme. The considered model is proposed under the Caputo power law derivative of fractional order. Further, in the considered model by utilizing the time esteem of cash rule, we build up break even with vital and interest mortgage model that gives quickest installment plan with the least interest rate. The proposed scheme is based on some operational matrices of integration and differentiation of fractional order. For the required operational matrices, we use shifted Legendre polynomials. With the help of the operational matrices, we establish a numerical algorithm to convert the considered model to a system of Lyapunov matrix equation. By using Matlab, we then solve the resultant algebraic equation to get the required solution in numerical form. Further, we plot the approximate solution for various fractional order graphically. |
| first_indexed | 2024-03-13T08:23:25Z |
| format | Article |
| id | doaj.art-1b5fa30dbeb04b938118c21c7a5e257e |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-03-13T08:23:25Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-1b5fa30dbeb04b938118c21c7a5e257e2023-05-31T04:47:32ZengElsevierResults in Applied Mathematics2590-03742023-05-0118100367A numerical scheme for fractional order mortgage model of economicsHafsa Naz0Thongchai Dumrongpokaphan1Thanin Sitthiwirattham2Hussam Alrabaiah3Khursheed J. Ansari4Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, PakistanResearch Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandMathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand; Corresponding author.College of Engineering, Al Ain University, Al Ain, United Arab Emirates; Department of Mathematics, Tafila Technical University, Tafila, JordanDepartment of Mathematics, College of Science, King Khalid University 61413, Abha, Saudi ArabiaIn this article, the famous mortgage model of economics is investigated by developing a numerical scheme. The considered model is proposed under the Caputo power law derivative of fractional order. Further, in the considered model by utilizing the time esteem of cash rule, we build up break even with vital and interest mortgage model that gives quickest installment plan with the least interest rate. The proposed scheme is based on some operational matrices of integration and differentiation of fractional order. For the required operational matrices, we use shifted Legendre polynomials. With the help of the operational matrices, we establish a numerical algorithm to convert the considered model to a system of Lyapunov matrix equation. By using Matlab, we then solve the resultant algebraic equation to get the required solution in numerical form. Further, we plot the approximate solution for various fractional order graphically.http://www.sciencedirect.com/science/article/pii/S2590037423000134Shifted Legendre polynomialsOperational matricesMortgage modelFractional-order differential equations |
| spellingShingle | Hafsa Naz Thongchai Dumrongpokaphan Thanin Sitthiwirattham Hussam Alrabaiah Khursheed J. Ansari A numerical scheme for fractional order mortgage model of economics Results in Applied Mathematics Shifted Legendre polynomials Operational matrices Mortgage model Fractional-order differential equations |
| title | A numerical scheme for fractional order mortgage model of economics |
| title_full | A numerical scheme for fractional order mortgage model of economics |
| title_fullStr | A numerical scheme for fractional order mortgage model of economics |
| title_full_unstemmed | A numerical scheme for fractional order mortgage model of economics |
| title_short | A numerical scheme for fractional order mortgage model of economics |
| title_sort | numerical scheme for fractional order mortgage model of economics |
| topic | Shifted Legendre polynomials Operational matrices Mortgage model Fractional-order differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S2590037423000134 |
| work_keys_str_mv | AT hafsanaz anumericalschemeforfractionalordermortgagemodelofeconomics AT thongchaidumrongpokaphan anumericalschemeforfractionalordermortgagemodelofeconomics AT thaninsitthiwirattham anumericalschemeforfractionalordermortgagemodelofeconomics AT hussamalrabaiah anumericalschemeforfractionalordermortgagemodelofeconomics AT khursheedjansari anumericalschemeforfractionalordermortgagemodelofeconomics AT hafsanaz numericalschemeforfractionalordermortgagemodelofeconomics AT thongchaidumrongpokaphan numericalschemeforfractionalordermortgagemodelofeconomics AT thaninsitthiwirattham numericalschemeforfractionalordermortgagemodelofeconomics AT hussamalrabaiah numericalschemeforfractionalordermortgagemodelofeconomics AT khursheedjansari numericalschemeforfractionalordermortgagemodelofeconomics |