A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system
Abstract We investigate a fractional energy supply–demand system (ES–DS) model using power-law-type kernels and advanced operators called fractal-fractional operators with a couple of fractal and fractional orders. It is established that for the fractal-fractional model of the ES–DS, a solution exis...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02057-z |
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| author | Salah Boulaaras Tanzeela Kanwal İbrahim Avcı Sina Etemad Zaher Mundher Yaseen |
| author_facet | Salah Boulaaras Tanzeela Kanwal İbrahim Avcı Sina Etemad Zaher Mundher Yaseen |
| author_sort | Salah Boulaaras |
| collection | DOAJ |
| description | Abstract We investigate a fractional energy supply–demand system (ES–DS) model using power-law-type kernels and advanced operators called fractal-fractional operators with a couple of fractal and fractional orders. It is established that for the fractal-fractional model of the ES–DS, a solution exists and it is unique. One of the principal innovations is to conduct the stability of the fractal-fractional-based ES–DS model. Moreover, after some theorems on the existence theory, we upgrade the Adams–Bashforth (AB) method in the context of the fractal-fractional-based operators and simulate the graphs for varied data on the fractal and fractional orders when we explored the stability requirements in four variants to approach the required numerical solutions. Next, by removing the fractal order, we transform our fractal-fractional-based ES–DS model to a fractional Caputo-type model, and then, a numerical methodology known as the Taylor operational matrix method is applied to simulate new graphs and compare them to previous fractal-fractional-based model. |
| format | Article |
| id | doaj-art-d2c3c42701db44d89ffe4762199d1023 |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-d2c3c42701db44d89ffe4762199d10232025-08-20T01:49:47ZengSpringerOpenBoundary Value Problems1687-27702025-05-012025113210.1186/s13661-025-02057-zA study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand systemSalah Boulaaras0Tanzeela Kanwal1İbrahim Avcı2Sina Etemad3Zaher Mundher Yaseen4Department of Mathematics, College of Science, Qassim UniversityDepartment of Mathematics, University of SargodhaDepartment of Basic Sciences and Humanities, Faculty of Arts and Sciences, Cyprus International UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityCivil and Environmental Engineering Department, King Fahd University of Petroleum & MineralsAbstract We investigate a fractional energy supply–demand system (ES–DS) model using power-law-type kernels and advanced operators called fractal-fractional operators with a couple of fractal and fractional orders. It is established that for the fractal-fractional model of the ES–DS, a solution exists and it is unique. One of the principal innovations is to conduct the stability of the fractal-fractional-based ES–DS model. Moreover, after some theorems on the existence theory, we upgrade the Adams–Bashforth (AB) method in the context of the fractal-fractional-based operators and simulate the graphs for varied data on the fractal and fractional orders when we explored the stability requirements in four variants to approach the required numerical solutions. Next, by removing the fractal order, we transform our fractal-fractional-based ES–DS model to a fractional Caputo-type model, and then, a numerical methodology known as the Taylor operational matrix method is applied to simulate new graphs and compare them to previous fractal-fractional-based model.https://doi.org/10.1186/s13661-025-02057-zInitial value problemFractal-fractional derivativeExistence resultsStability analysisMathematical modeling |
| spellingShingle | Salah Boulaaras Tanzeela Kanwal İbrahim Avcı Sina Etemad Zaher Mundher Yaseen A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system Boundary Value Problems Initial value problem Fractal-fractional derivative Existence results Stability analysis Mathematical modeling |
| title | A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system |
| title_full | A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system |
| title_fullStr | A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system |
| title_full_unstemmed | A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system |
| title_short | A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system |
| title_sort | study on the existence of unique stable approximate solutions fractal fractional based model of an energy supply demand system |
| topic | Initial value problem Fractal-fractional derivative Existence results Stability analysis Mathematical modeling |
| url | https://doi.org/10.1186/s13661-025-02057-z |
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