Results 61 to 70 of about 302 (175)

Some new results for the generalized bivariate Fibonacci and Lucas polynomials [PDF]

Mathematica Moravica
In this paper, new identities are obtained by using the generalized bivariate Fibonacci and Lucas polynomials. Firstly, several binomial summations and the closed formulas for summation of powers are investigated for these polynomials.
Yılmaz Nazmıye
doaj   +1 more source

Computational analysis of time-fractional models in energy infrastructure applications

Alexandria Engineering Journal, 2023
In this paper, we propose an effective numerical method to solve the one- and two-dimensional time-fractional convection-diffusion equations based on the Caputo derivative.
Imtiaz Ahmad, Asmidar Abu Bakar, Ihteram Ali, Sirajul Haq, Salman Yussof, Ali Hasan Ali   +5 more
doaj   +1 more source

FPGA Realization of a Novel Hyperchaos Augmented Image Encryption Algorithm

IET Computers &Digital Techniques, Volume 2026, Issue 1, 2026.
With the rapid growth of multimedia communication, protecting image data has become increasingly critical. This article proposes a novel 3‐stage hyperchaos‐based augmented image encryption technique (3SHAIET) that utilizes a three‐stage process with chaotic systems of increasing dimensionality (e.g., six‐dimensional [6D], 8D, and 9D) to enhance ...
Wassim Alexan, Noura H. Elshabasy, Eyad Mamdouh, Remas Osama, Mohamed A. Abd El Ghany, Dina El-Damak, Jim Harkin   +6 more
wiley   +1 more source

New convolved Fibonacci collocation procedure for the Fitzhugh–Nagumo non-linear equation

Nonlinear Engineering
This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo equation. The proposed solution is expressed as a double sum of basis functions that are chosen to be the convolved Fibonacci polynomials that generalize the well-
Abd-Elhameed Waleed Mohamed, Al-Harbi Mohamed Salem, Atta Ahmed Gamal   +2 more
doaj   +1 more source

A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully, A. Al-Kateeb, Abdul Rauf Khan   +2 more
wiley   +1 more source

2-Fibonacci polynomials in the family of Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2018
In the present study, we define new 2-Fibonacci polynomials by using terms of a new family of Fibonacci numbers given in [4]. We show that there is a relationship between the coefficient of the 2-Fibonacci polynomials and Pascal's triangle. We give some identities of the 2-Fibonacci polynomials.
Ozkan, Engin, Tastan, Merve, Aydogdu, Ali   +2 more
openaire   +2 more sources

Computational Framework for Numerical Simulation of Fractional‐Order Financial Crime Model via Lucas Collocation Technique

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Lucas collocation approach is used in this study to approximate a fractional‐order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned.
Mahmoud Abd El-Hady, Homan Emadifar, Mehdi Hariri, Atallah El-Shenawy, Chong Lin   +4 more
wiley   +1 more source

Symmetric and generating functions of generalized (p,q)-numbers

Kuwait Journal of Science, 2021
In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba, Ali Boussayoud, Abdelhamid Abderrezzak   +2 more
doaj   +1 more source

Leonardo Cartan Numbers and Related Fibonacci–Lucas Structures

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper investigates the Leonardo Cartan numbers, defined as an extension of the classical Leonardo sequence through additional algebraic structures. The recurrence relations of these numbers are established, and various summation formulas are derived.
Hasan Çakır, İskender Öztürk, Smritijit Sen   +2 more
wiley   +1 more source

Bernoulli-Fibonacci Polynomials

, 2020
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and numbers are studied in parallel with usual Bernoulli counterparts.
Pashaev, Oktay K., Ozvatan, Merve
openaire   +2 more sources