An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations
This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-05-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447924000534 |
| _version_ | 1797243049775988736 |
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| author | Sivalingam S M Pushpendra Kumar V. Govindaraj Raed Ali Qahiti Waleed Hamali Zico Meetei Mutum |
| author_facet | Sivalingam S M Pushpendra Kumar V. Govindaraj Raed Ali Qahiti Waleed Hamali Zico Meetei Mutum |
| author_sort | Sivalingam S M |
| collection | DOAJ |
| description | This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with generalized Caputo-type derivatives were reduced into a system of algebraic equations, which was further solved to obtain the unknown solution. The convergence and error bounds are theoretically calculated. The results are quantitatively confirmed in various cases. To demonstrate the correctness and computational efficacy of this proposed technique, it is compared to other well-known methods. |
| first_indexed | 2024-04-24T18:48:56Z |
| format | Article |
| id | doaj.art-c7171a9ee69d4d6496b420d6e438ef39 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-04-24T18:48:56Z |
| publishDate | 2024-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-c7171a9ee69d4d6496b420d6e438ef392024-03-27T04:51:54ZengElsevierAin Shams Engineering Journal2090-44792024-05-01155102678An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equationsSivalingam S M0Pushpendra Kumar1V. Govindaraj2Raed Ali Qahiti3Waleed Hamali4Zico Meetei Mutum5Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, IndiaDepartment of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey; Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, TurkeyDepartment of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, IndiaDepartment of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia; Corresponding author.This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with generalized Caputo-type derivatives were reduced into a system of algebraic equations, which was further solved to obtain the unknown solution. The convergence and error bounds are theoretically calculated. The results are quantitatively confirmed in various cases. To demonstrate the correctness and computational efficacy of this proposed technique, it is compared to other well-known methods.http://www.sciencedirect.com/science/article/pii/S2090447924000534Fractal-fractional derivativesVieta-Fibonacci polynomialsOperational matrixConvergenceError bound |
| spellingShingle | Sivalingam S M Pushpendra Kumar V. Govindaraj Raed Ali Qahiti Waleed Hamali Zico Meetei Mutum An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations Ain Shams Engineering Journal Fractal-fractional derivatives Vieta-Fibonacci polynomials Operational matrix Convergence Error bound |
| title | An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations |
| title_full | An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations |
| title_fullStr | An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations |
| title_full_unstemmed | An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations |
| title_short | An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations |
| title_sort | operational matrix approach with vieta fibonacci polynomial for solving generalized caputo fractal fractional differential equations |
| topic | Fractal-fractional derivatives Vieta-Fibonacci polynomials Operational matrix Convergence Error bound |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924000534 |
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