A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations
In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient tr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3985 |
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| author | Abdelkader Moumen Abdelaziz Mennouni Mohamed Bouye |
| author_facet | Abdelkader Moumen Abdelaziz Mennouni Mohamed Bouye |
| author_sort | Abdelkader Moumen |
| collection | DOAJ |
| description | In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient transformation reduces the problem to a system of two independent equations. Solving two algebraic equations yields an approximate solution to the problem. The proposed method’s efficiency and accuracy are validated. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests reinforce the interpretations of the theory. |
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| format | Article |
| id | doaj.art-b3db91adb8724779bbcaf701d097142f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:29:18Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b3db91adb8724779bbcaf701d097142f2023-11-19T11:50:20ZengMDPI AGMathematics2227-73902023-09-011118398510.3390/math11183985A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential EquationsAbdelkader Moumen0Abdelaziz Mennouni1Mohamed Bouye2Department of Mathematics, Faculty of Sciences, University of Ha’il, Ha’il 55425, Saudi ArabiaDepartment of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaIn this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient transformation reduces the problem to a system of two independent equations. Solving two algebraic equations yields an approximate solution to the problem. The proposed method’s efficiency and accuracy are validated. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests reinforce the interpretations of the theory.https://www.mdpi.com/2227-7390/11/18/3985integrodifferential equationssystemfractionalVieta–Fibonacci polynomialsprojection method |
| spellingShingle | Abdelkader Moumen Abdelaziz Mennouni Mohamed Bouye A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations Mathematics integrodifferential equations system fractional Vieta–Fibonacci polynomials projection method |
| title | A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations |
| title_full | A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations |
| title_fullStr | A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations |
| title_full_unstemmed | A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations |
| title_short | A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations |
| title_sort | novel vieta fibonacci projection method for solving a system of fractional integrodifferential equations |
| topic | integrodifferential equations system fractional Vieta–Fibonacci polynomials projection method |
| url | https://www.mdpi.com/2227-7390/11/18/3985 |
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