A survey of fractional calculus applications in artificial neural networks

M Joshi, S Bhosale, VA Vyawahare - Artificial Intelligence Review, 2023 - Springer
Artificial neural network (ANN) is the backbone of machine learning, specifically deep
learning. The interpolating and learning ability of an ANN makes it an ideal tool for …

Multistable dynamics in a Hopfield neural network under electromagnetic radiation and dual bias currents

Q Wan, Z Yan, F Li, J Liu, S Chen - Nonlinear Dynamics, 2022 - Springer
This paper investigates a Hopfield neural network under the simulation of external
electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux …

Incommensurate fractional discrete neural network: chaos and complexity

A Abbes, A Ouannas, N Shawagfeh… - The European Physical …, 2022 - Springer
In this research, we offer a novel discrete-time fractional Hopfield neural network (DTHNN)
with incommensurate order. Analytical and numerical analysis by employing maximum …

Further investigation on bifurcation and their control of fractional‐order bidirectional associative memory neural networks involving four neurons and multiple delays

C Xu, W Zhang, C Aouiti, Z Liu… - … Methods in the Applied …, 2023 - Wiley Online Library
This work principally probes into the stability, the existence, and control of Hopf bifurcation of
new established fractional‐order delayed bidirectional associative memory (BAM) neural …

[HTML][HTML] An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses

YM Chu, T Alzahrani, S Rashid, W Rashidah… - Scientific Reports, 2023 - nature.com
The multiple activities of neurons frequently generate several spiking-bursting variations
observed within the neurological mechanism. We show that a discrete fractional-order …

[HTML][HTML] The new fractional discrete neural network model under electromagnetic radiation: Chaos, control and synchronization

AS Heilat, RC Karoun, A Al-Husban, A Abbes… - Alexandria Engineering …, 2023 - Elsevier
This paper describes a new four-dimensional fractional discrete neural network with
electromagnetic radiation model. In addition, the non-linear dynamics of the suggested …

Practical stability criteria for discrete fractional neural networks in product form design analysis

T Stamov - Chaos, Solitons & Fractals, 2024 - Elsevier
In this paper, a neural network approach is suggested to the product design analysis.
Namely, fractional-order neural network models are proposed as more flexible mechanism …

Finite-Time Stability of Fractional-Order Discontinuous Nonlinear Systems With State-Dependent Delayed Impulses

G Palanisamy, A Kashkynbayev… - IEEE Transactions on …, 2023 - ieeexplore.ieee.org
This article investigates finite-time stability (FTS) and finite-time contractive stability (FTCS)
of discontinuous nonlinear fractional-order (FO) systems with time-delay and state …

[HTML][HTML] Robust stabilization and synchronization of a novel chaotic system with input saturation constraints

AT Azar, FE Serrano, Q Zhu, M Bettayeb, G Fusco, J Na… - Entropy, 2021 - mdpi.com
In this paper, the robust stabilization and synchronization of a novel chaotic system are
presented. First, a novel chaotic system is presented in which this system is realized by …

[HTML][HTML] Extreme multistability of a fractional-order discrete-time neural network

AO Almatroud - Fractal and Fractional, 2021 - mdpi.com
At present, the extreme multistability of fractional order neural networks are gaining much
interest from researchers. In this paper, by utilizing the fractional ℑ-Caputo operator, a …