On highly efficient fractional numerical method for solving nonlinear engineering models

M Shams, B Carpentieri - Mathematics, 2023 - mdpi.com
We proposed and analyzed the fractional simultaneous technique for approximating all the
roots of nonlinear equations in this research study. The newly developed fractional Caputo …

Robust and accurate numerical framework for multi-dimensional fractional-order telegraph equations using Jacobi/Jacobi-Romanovski spectral technique

MA Abdelkawy, M Izadi, W Adel - Boundary Value Problems, 2024 - Springer
This paper presents a novel spectral algorithm for the numerical solution of multi-
dimensional fractional-order telegraph equations, a critical model used to capture the …

Fractional Order Bifurcation and Chaos of Aeroelastic Aerofoil System with Multiple Stiffness Nonlinearities

T Degefa, B Ramakrishnan, Y Admassu… - International Journal of …, 2024 - Elsevier
This paper presents a novel exploration of bifurcation and chaos dynamics in 2D fractional
order aeroelastic aerofoil systems (FOAAS) operating in incompressible flow, with a …

[PDF][PDF] First Derivative Approximations and Applications

Y Dimitrov, S Georgiev, V Todorov - Fractal and Fractional, 2024 - preprints.org
In this paper we consider constructions of first derivative approximations using the
generating function. The weights of the approximations contain the powers of a parameter …

[HTML][HTML] Influence of Fractional Order on the Behavior of a Normalized Time-Fractional SIR Model

J Kim - Mathematics, 2024 - mdpi.com
In this paper, we propose a novel normalized time-fractional susceptible–infected–removed
(SIR) model that incorporates memory effects into epidemiological dynamics. The proposed …

[HTML][HTML] Artificial hybrid neural network-based simultaneous scheme for solving nonlinear equations: Applications in engineering

M Shams, N Kausar, S Araci, GI Oros - Alexandria Engineering Journal, 2024 - Elsevier
A novel three-step simultaneous scheme for finding all distinct and multiple roots of non-
linear equations are developed in this paper. Analysis of convergence demonstrates that the …