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 …

Exponentially stable periodic oscillation and Mittag–Leffler stabilization for fractional-order impulsive control neural networks with piecewise Caputo derivatives

T Zhang, J Zhou, Y Liao - IEEE Transactions on Cybernetics, 2021 - ieeexplore.ieee.org
It is well known that the conventional fractional-order neural networks (FONNs) cannot
generate nonconstant periodic oscillation. For this point, this article discusses a class of …

Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects

H Zhang, Y Cheng, H Zhang, W Zhang, J Cao - … and Computers in …, 2022 - Elsevier
This article discusses the global Mittag-Leffler projective synchronization (GM-LPS) on
fractional-order quaternion-valued neural networks (FOQVNNs) including mixed delays and …

New exploration on bifurcation in fractional-order genetic regulatory networks incorporating both type delays

P Li, Y Li, R Gao, C Xu, Y Shang - The European Physical Journal Plus, 2022 - Springer
This study principally deals with the stability property and the emergence of Hopf bifurcation
for fractional-order genetic regulatory networks incorporating distributed delays and discrete …

Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique

GC Wu, T Abdeljawad, J Liu, D Baleanu, KT Wu - 2019 - earsiv.cankaya.edu.tr
A class of semilinear fractional difference equations is introduced in this paper. The fixed
point theorem is adopted to find stability conditions for fractional difference equations. The …

Finite-time synchronization of fractional-order gene regulatory networks with time delay

Y Qiao, H Yan, L Duan, J Miao - Neural Networks, 2020 - Elsevier
As multi-gene networks transmit signals and products by synchronous cooperation,
investigating the synchronization of gene regulatory networks may help us to explore the …

Mittag–Leffler stability and synchronization of neutral-type fractional-order neural networks with leakage delay and mixed delays

CA Popa - Journal of the Franklin Institute, 2023 - Elsevier
In recent years, there have been a lot of studies focusing on the dynamics of fractional-order
neural networks (FONNs). One problem is that the standard Lyapunov theory does not apply …

Finite-time nonchattering synchronization of coupled neural networks with multi-weights

LH Zhao, S Wen, Z Guo, K Shi, J Xiao… - … on Network Science …, 2023 - ieeexplore.ieee.org
This paper is concerned with finite-time synchronization and finite-time synchronization for
coupled neural networks with multiple state/derivative couplings. Firstly, several sufficient …

Synchronization analysis of fractional-order inertial-type neural networks with time delays

Q Peng, J Jian - Mathematics and Computers in Simulation, 2023 - Elsevier
This paper is dedicated to the global Mittag-Leffler synchronization (GMLS) of fractional-
order inertial-type neural networks (FOITNNs) with time delays. To begin with, based on the …

Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control

S Aadhithiyan, R Raja, Q Zhu, J Alzabut… - Chaos, Solitons & …, 2021 - Elsevier
Adaptive modified projective function synchronization of non-linear distributive fractional
order complex dynamical networks (DFCDN) is addressed in this paper. Firstly, we have …