Results 21 to 30 of about 9,574,302 (235)

Stability and Stabilization of 2D Linear Discrete Systems with Fractional Orders Based on the Discrimination System of Polynomials

Mathematics, 2022
This paper considers the stability and stabilization of two-dimensional (2D) fractional-order systems described by state-space model based on the discrimination system of polynomials. Necessary and sufficient conditions of stability and stabilization are
Xiaoxue Li, Xiaorong Hou, Jing Yang, Min Luo   +3 more
doaj   +1 more source

Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation

Demonstratio Mathematica, 2023
The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders.
A. A. El-Sayed
semanticscholar   +1 more source

An accurate operational matrix method based on Lagrange polynomials for solving fractional-order pantograph delay and Riccati differential equations

Physica Scripta, 2023
This paper introduces the fractional-order Lagrange polynomials approach to solve initial value problems for pantograph delay and Riccati differential equations involving fractional-order derivatives.
Saurabh Kumar, V. Gupta, Ajay Mahaputra Kumar, J. Gómez-Aguilar   +3 more
semanticscholar   +1 more source

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

IEEE Access, 2022
Chaotic systems are widely used in signal and image encryption schemes. Therefore, the design of new chaotic systems is always useful for improving the performance of encryption schemes in terms of security. In this work, we first demonstrate the chaotic
A. Daoui, M. Yamni, H. Karmouni, M. Sayyouri, H. Qjidaa, Musheer Ahmad, A. A. Abd El-Latif   +6 more
semanticscholar   +1 more source

Semi-Analytical Solutions for Some Types of Nonlinear Fractional-Order Differential Equations Based on Third-Kind Chebyshev Polynomials

Fractal and Fractional, 2023
Approximate solutions for a family of nonlinear fractional-order differential equations are introduced in this work. The fractional-order operator of the derivative are provided in the Caputo sense.
Adel Abd Elaziz El-Sayed, Salah Boulaaras, Mohammed AbaOud   +2 more
doaj   +1 more source

Numerical Study of Caputo Fractional-Order Differential Equations by Developing New Operational Matrices of Vieta–Lucas Polynomials

Fractal and Fractional, 2022
In this article, we develop a numerical method based on the operational matrices of shifted Vieta–Lucas polynomials (VLPs) for solving Caputo fractional-order differential equations (FDEs).
Zulfiqar Ahmad Noor, Imran Talib, T. Abdeljawad, Manar A. Alqudah   +3 more
semanticscholar   +1 more source

New fractional-order shifted Gegenbauer moments for image analysis and recognition

Journal of Advanced Research, 2020
Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments.
Khalid M. Hosny, Mohamed M. Darwish, Mohamed Meselhy Eltoukhy   +2 more
doaj   +1 more source

Romanovski–Jacobi polynomials for the numerical solution of multi-dimensional multi-order time fractional telegraph equations

Results in Physics, 2023
In this paper, the one- and two-dimensional multi-order time fractional telegraph equations are introduced. Two collocation methods based on the one- and two-dimensional Romanovski–Jacobi polynomials are proposed to solve them.
J. Nazari, M.H. Heydari, M. Hosseininia
doaj   +1 more source

Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations

Advances in Mathematical Physics, 2020
Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials.
Haidong Qu, Xiaopeng Yang, Zihang She
doaj   +1 more source

Numerical solution of two-dimensional fractional-order partial differential equations using hybrid functions

Partial Differential Equations in Applied Mathematics, 2021
Fractional differential equations fit perfectly into nature modeling, requiring the finding of efficient numerical methods of solving them. This paper aims to propose a method for solving two-dimensional fractional order equations by constructing a new ...
Octavian Postavaru, Antonela Toma
doaj   +1 more source