Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials
This study introduces a novel method using the Müntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials are used to approximate the state and control...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4440_e1f3bc12f05dc3c2131d3b449c31350a.pdf |
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| _version_ | 1841560218289307648 |
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| author | Mohammad Sahabi Allahbakhsh Yazdani Cherati |
| author_facet | Mohammad Sahabi Allahbakhsh Yazdani Cherati |
| author_sort | Mohammad Sahabi |
| collection | DOAJ |
| description | This study introduces a novel method using the Müntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials are used to approximate the state and control variables in the considered problems. Consequently, the fractional optimal control problem is transformed into a nonlinear programming problem through collocation points, yielding unknown coefficients. To achieve this, stable and efficient methods for calculating the fractional integral and derivative operators of Müntz-Legendre functions based on three-term recurrence formulas and Jacobi-Gauss quadrature rules are presented. A thorough convergence analysis, along with error estimates, is provided. Several numerical examples are included to demonstrate the efficiency and accuracy of the proposed method. |
| format | Article |
| id | doaj-art-c9902ee7ce9c456ab9834d3a0a2c9f6b |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-c9902ee7ce9c456ab9834d3a0a2c9f6b2025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114118921710.22103/jmmr.2024.22811.15654440Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomialsMohammad Sahabi0Allahbakhsh Yazdani Cherati1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar IranThis study introduces a novel method using the Müntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials are used to approximate the state and control variables in the considered problems. Consequently, the fractional optimal control problem is transformed into a nonlinear programming problem through collocation points, yielding unknown coefficients. To achieve this, stable and efficient methods for calculating the fractional integral and derivative operators of Müntz-Legendre functions based on three-term recurrence formulas and Jacobi-Gauss quadrature rules are presented. A thorough convergence analysis, along with error estimates, is provided. Several numerical examples are included to demonstrate the efficiency and accuracy of the proposed method.https://jmmrc.uk.ac.ir/article_4440_e1f3bc12f05dc3c2131d3b449c31350a.pdfmüntz-legendre polynomialsfractional optimal control problemsconvergence analysisnumerical techniques |
| spellingShingle | Mohammad Sahabi Allahbakhsh Yazdani Cherati Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials Journal of Mahani Mathematical Research müntz-legendre polynomials fractional optimal control problems convergence analysis numerical techniques |
| title | Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials |
| title_full | Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials |
| title_fullStr | Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials |
| title_full_unstemmed | Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials |
| title_short | Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials |
| title_sort | numerical solutions for fractional optimal control problems using muntz legendre polynomials |
| topic | müntz-legendre polynomials fractional optimal control problems convergence analysis numerical techniques |
| url | https://jmmrc.uk.ac.ir/article_4440_e1f3bc12f05dc3c2131d3b449c31350a.pdf |
| work_keys_str_mv | AT mohammadsahabi numericalsolutionsforfractionaloptimalcontrolproblemsusingmuntzlegendrepolynomials AT allahbakhshyazdanicherati numericalsolutionsforfractionaloptimalcontrolproblemsusingmuntzlegendrepolynomials |