On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis
This paper introduces a general nabla operator of order two that includes coefficients of various trigonometric functions. We also introduce its inverse, which leads us to derive the second-order $ \overline{\theta({\tt{t}})} $-Fibonacci polynomial, sequence, and its summation. Here, we have obtaine...
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| Language: | English |
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AIMS Press
2025-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025046 |
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| author | Rajiniganth Pandurangan Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez |
| author_facet | Rajiniganth Pandurangan Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez |
| author_sort | Rajiniganth Pandurangan |
| collection | DOAJ |
| description | This paper introduces a general nabla operator of order two that includes coefficients of various trigonometric functions. We also introduce its inverse, which leads us to derive the second-order $ \overline{\theta({\tt{t}})} $-Fibonacci polynomial, sequence, and its summation. Here, we have obtained the derivative of the $ \overline{\theta({\tt{t}})} $-Fibonacci polynomial using a proportional derivative. Furthermore, this study presents derived theorems and intriguing findings on the summation of terms in the second-order Fibonacci sequence, and we have investigated the bifurcation analysis of the $ \overline{\theta({\tt{t}})} $-Fibonacci generating function. In addition, we have included appropriate examples to demonstrate our findings by using MATLAB. |
| format | Article |
| id | doaj-art-522bf4b71dae4a5f99ef5ffca8a11a3b |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-522bf4b71dae4a5f99ef5ffca8a11a3b2025-08-20T02:48:13ZengAIMS PressAIMS Mathematics2473-69882025-01-0110197298710.3934/math.2025046On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysisRajiniganth Pandurangan0Sabri T. M. Thabet1Imed Kedim2Miguel Vivas-Cortez3Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University, Samayapuram, Tamil Nadu, 621112, IndiaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, IndiaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaFaculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Sede Quito, EcuadorThis paper introduces a general nabla operator of order two that includes coefficients of various trigonometric functions. We also introduce its inverse, which leads us to derive the second-order $ \overline{\theta({\tt{t}})} $-Fibonacci polynomial, sequence, and its summation. Here, we have obtained the derivative of the $ \overline{\theta({\tt{t}})} $-Fibonacci polynomial using a proportional derivative. Furthermore, this study presents derived theorems and intriguing findings on the summation of terms in the second-order Fibonacci sequence, and we have investigated the bifurcation analysis of the $ \overline{\theta({\tt{t}})} $-Fibonacci generating function. In addition, we have included appropriate examples to demonstrate our findings by using MATLAB.https://www.aimspress.com/article/doi/10.3934/math.2025046generalized nabla operator variable coefficientsfibonacci sequencefibonacci summationproportional $ \alpha $-derivativebifurcation |
| spellingShingle | Rajiniganth Pandurangan Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis AIMS Mathematics generalized nabla operator variable coefficients fibonacci sequence fibonacci summation proportional $ \alpha $-derivative bifurcation |
| title | On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis |
| title_full | On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis |
| title_fullStr | On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis |
| title_full_unstemmed | On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis |
| title_short | On the Generalized $ \overline{\theta({\tt{t}})} $-Fibonacci sequences and its bifurcation analysis |
| title_sort | on the generalized overline theta tt t fibonacci sequences and its bifurcation analysis |
| topic | generalized nabla operator variable coefficients fibonacci sequence fibonacci summation proportional $ \alpha $-derivative bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025046 |
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