Dickson polynomial-based solutions for fractional order physics problems
Abstract In this article, we introduce a new operational matrix of the fractional-order derivative that depends on the Caputo operator of differentiation and first-kind Dickson polynomials. The established matrix, in addition to the Tau spectral method, will be used for solving three important appli...
| Published in: | Journal of Inequalities and Applications |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-09-01
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| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03367-7 |
| _version_ | 1848766261632172032 |
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| author | A. A. El-Sayed S. Boulaaras F. A. Al-Kharousi |
| author_facet | A. A. El-Sayed S. Boulaaras F. A. Al-Kharousi |
| author_sort | A. A. El-Sayed |
| collection | DOAJ |
| container_title | Journal of Inequalities and Applications |
| description | Abstract In this article, we introduce a new operational matrix of the fractional-order derivative that depends on the Caputo operator of differentiation and first-kind Dickson polynomials. The established matrix, in addition to the Tau spectral method, will be used for solving three important applications in the fractional-order forms: the Bagley-Torvik problem, the Lane-Emden type equation, and Bratu’s problem. The primary approach for addressing these applications involves transforming the fractional-order problem and its conditions into a system of algebraic equations with unknown coefficients. The error estimation and convergence analysis of the proposed method will be thoroughly examined. Our proposed technique will be applied through some examples with comparisons. The introduced numerical results support the theoretical ones, in addition to demonstrating the accuracy and applicability of the suggested method. |
| format | Article |
| id | doaj-art-4732833cdf9a4ca7a00a2fdd19ab4d6c |
| institution | Directory of Open Access Journals |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| spelling | doaj-art-4732833cdf9a4ca7a00a2fdd19ab4d6c2025-10-06T07:46:18ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-09-012025112210.1186/s13660-025-03367-7Dickson polynomial-based solutions for fractional order physics problemsA. A. El-Sayed0S. Boulaaras1F. A. Al-Kharousi2Department of Mathematics, College of Education, University of Technology and Applied SciencesDepartment of Mathematics, College of Sciences, Qassim UniversityDepartment of Mathematics, College of Education, University of Technology and Applied SciencesAbstract In this article, we introduce a new operational matrix of the fractional-order derivative that depends on the Caputo operator of differentiation and first-kind Dickson polynomials. The established matrix, in addition to the Tau spectral method, will be used for solving three important applications in the fractional-order forms: the Bagley-Torvik problem, the Lane-Emden type equation, and Bratu’s problem. The primary approach for addressing these applications involves transforming the fractional-order problem and its conditions into a system of algebraic equations with unknown coefficients. The error estimation and convergence analysis of the proposed method will be thoroughly examined. Our proposed technique will be applied through some examples with comparisons. The introduced numerical results support the theoretical ones, in addition to demonstrating the accuracy and applicability of the suggested method.https://doi.org/10.1186/s13660-025-03367-7Dickson polynomialsCaputo fractional operatorOperational matrix of fractional derivativesTau methodBagley-Torvik equationLane-Emden problem |
| spellingShingle | A. A. El-Sayed S. Boulaaras F. A. Al-Kharousi Dickson polynomial-based solutions for fractional order physics problems Dickson polynomials Caputo fractional operator Operational matrix of fractional derivatives Tau method Bagley-Torvik equation Lane-Emden problem |
| title | Dickson polynomial-based solutions for fractional order physics problems |
| title_full | Dickson polynomial-based solutions for fractional order physics problems |
| title_fullStr | Dickson polynomial-based solutions for fractional order physics problems |
| title_full_unstemmed | Dickson polynomial-based solutions for fractional order physics problems |
| title_short | Dickson polynomial-based solutions for fractional order physics problems |
| title_sort | dickson polynomial based solutions for fractional order physics problems |
| topic | Dickson polynomials Caputo fractional operator Operational matrix of fractional derivatives Tau method Bagley-Torvik equation Lane-Emden problem |
| url | https://doi.org/10.1186/s13660-025-03367-7 |
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