Results 41 to 50 of about 466,283 (262)

The Fibonacci polynomials solution for Abel’s integral equation of second kind [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2020
We suggest a convenient method based on the Fibonacci polynomials and the collocation points for solving approximately the Abel’s integral equation of second kind.
H. Deilami Azodi
doaj   +1 more source

The generalized k-Fibonacci polynomials and generalized k-Lucas polynomials

Notes on Number Theory and Discrete Mathematics, 2021
In this paper, we define new families of Generalized Fibonacci polynomials and Generalized Lucas polynomials and develop some elegant properties of these families.
Merve Taştan, E. Özkan, A. Shannon
semanticscholar   +1 more source

Fibonacci polynomials

Pure and Applied Mathematics Quarterly
The Fibonacci polynomials $\big\{F_n(x)\big\}_{n\ge 0}$ have been studied in multiple ways. In this paper we study them by means of the theory of Heaps of Viennot. In this setting our polynomials form a basis $\big\{P_n(x)\big\}_{n\ge 0}$ with $P_n(x)$ monic of degree $n$. This given, we are forced to set $P_n(x)=F_{n+1}(x)$.
Garsia, A., Ganzberger, G.
openaire   +2 more sources

A Study on Fibonacci and Lucas Bihypernomials

Discussiones Mathematicae - General Algebra and Applications, 2022
The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the ...
Szynal-Liana Anetta, Włoch Iwona
doaj   +1 more source

On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials

, 2012
We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences.
Andrews G E, Askey R, Atakishiyev N M, Bers L, Cigler J, Cigler J, Cigler J, Dahlquist G, Decio Levi, Dunlap R A, Ismail M E H, Lang W, Maroni P, Matveev V B, Natig Atakishiyev, Orlando Ragnisco, Pedro Franco, Schroeder M, Slater L J   +18 more
core   +1 more source

Fejér-Quadrature Collocation Algorithm for Solving Fractional Integro-Differential Equations via Fibonacci Polynomials

Contemporary Mathematics
In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to numerically solve both linear and nonlinear integro-differential equations with fractional-order derivatives. Our approach employs a quadrature-collocation method,
Youssri Hassan Youssri, A. G. Atta
semanticscholar   +1 more source

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

Mathematics
This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics.
Can Kızılateş, Wei-Shih Du, Nazlıhan Terzioğlu   +2 more
doaj   +1 more source

Novel Approach by Shifted Fibonacci Polynomials for Solving the Fractional Burgers Equation

Fractal and Fractional
This paper analyzes a novel use of the shifted Fibonacci polynomials (SFPs) to treat the time-fractional Burgers equation (TFBE). We first develop the fundamental formulas of these polynomials, which include their power series representation and the ...
Mohammed H. Alharbi, Abdullah F. Abu Sunayh, A. G. Atta, W. Abd-Elhameed   +3 more
semanticscholar   +1 more source

Distance Fibonacci Polynomials - Part II

Symmetry, 2021
In this paper we use a graph interpretation of distance Fibonacci polynomials to get a new generalization of Lucas polynomials in the distance sense.
U. Bednarz, M. Wołowiec-Musiał
semanticscholar   +1 more source

Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials

Ain Shams Engineering Journal, 2014
In this paper, we introduce a method to solve systems of linear Fredholm integro-differential equations in terms of Fibonacci polynomials. First, we present some properties of these polynomials then a new approach implementing a collocation method in ...
Farshid Mirzaee, Seyede Fatemeh Hoseini
doaj   +1 more source