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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025046 |
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| Summary: | 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. |
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| ISSN: | 2473-6988 |