Forced vibrations of nonlinear dynamical systems are usually predicted by solving differential equations, which have been derived from 'first principles' given by physical laws …
This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing …
The motivation behind this study is to simplify the complex mathematical formulations and reduce the time-consuming processes involved in traditional numerical methods for solving …
This article lucubrates the bifurcations in respect of a fractional-order neutral-type neural network (FONTNN) with two nonidentical delays. To begin with, the characteristic equation …
Differential equations play a significant role in modeling of real world dynamical problems. A large amount of prior physical information in the form of differential equations are inherited in …
The Boussinesq equation describes the model for horizontal water flow in unconfined aquifers without precipitation, a topic that has been extensively studied in the literature …
Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes …
Background Numerical methods are used to solve differential equations, but few are effective for nonlinear ordinary differential equations (ODEs) of order higher than one. This …
AK Sahoo, S Chakraverty - Computation and Modeling for Fractional Order …, 2024 - Elsevier
In this chapter, a neural network model for solving fractional differential equations is described. This model is based on approximating the solution by using power series …