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Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay

Abdulaziz Alofi, Jinde Cao, Ahmed Elaiw, Abdullah Al-Mazrooei
2014 Discrete Dynamics in Nature and Society  
This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay.  ...  Both the proposed criterion and an illustrative example show that the stability performance of Caputo fractional distributed delay neural networks is dependent on the time delay and the order of Caputo's  ...  The proposed criterion with an illustrative example shows that the stability performance of Caputo fractional neural networks with distributed delay is dependent on the time delay and the order of Caputo's  ... 
doi:10.1155/2014/529358 fatcat:e6jvtcahnrepfjrlshvsye52s4

Identification of Wind Turbine using Fractional Order Dynamic Neural Network and Optimization Algorithm

2020 International Journal of Engineering  
This complicated system dealing with wind behavior is identified by using a proposed fractional order dynamic neural network (FODNN) optimized with evolutionary computation.  ...  Furthermore, comparison of the results achieved by the proposed method and those of the integer order dynamic neural network (IODNN) depicts higher accuracy of the proposed FODNN.  ...  Fractional Calculus In this subsection, the main definitions of fractional calculus are briefly described along with the formulation used to FODNN model.  ... 
doi:10.5829/ije.2020.33.02b.12 fatcat:4m6epawrtnal3h57u5koet7zr4

Extreme Multistability of a Fractional-Order Discrete-Time Neural Network

A. Othman Almatroud
2021 Fractal and Fractional  
In this paper, by utilizing the fractional ℑ-Caputo operator, a simple fractional order discrete-time neural network with three neurons is introduced.  ...  At present, the extreme multistability of fractional order neural networks are gaining much interest from researchers.  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/fractalfract5040202 fatcat:w5uvpqcr55dobdnihetxhz5uiy

Fractional Calculus and Its Applications in Applied Mathematics and Other Sciences

Santanu Saha Ray, Abdon Atangana, S. C. Oukouomi Noutchie, Muhammet Kurulay, Necdet Bildik, Adem Kilicman
2014 Mathematical Problems in Engineering  
The issue contains eight research papers. The issue of robust stability for fractional order Hopfield neural networks with parameter uncertainties is rigorously investigated.  ...  This special issue on "Fractional Calculus and its Applications in Applied Mathematics and Other Sciences" is devoted to study the recent works in the above fields of fractional calculus done by the leading  ...  The issue contains eight research papers. The issue of robust stability for fractional order Hopfield neural networks with parameter uncertainties is rigorously investigated.  ... 
doi:10.1155/2014/849395 fatcat:tsyz3xgrwzg4zgxmn7cmxnpik4

Novel Results for the Stability of h-Discrete Fractional Neural Networks with Nonsingular and Nonlocal Kernels

Amel Hioual
2022 Innovative Journal of Mathematics (IJM)  
We investigate at a novel type of nonlinear discrete-time fractional neural networks using the h-discrete nabla ABC fractional operator.  ...  Furthermore, The Ulam-Hyers stability of the considered model, as well as significant findings, are shown.  ...  However, there are few results on the Ulam-Hyers stability of discrete-time fractional-order neural networks we state [35] , that investigated the Hyers-Ulam stability of a linear fractional neural network  ... 
doi:10.55059/ijm.2022.1.3/32 fatcat:7tmsyggadzd7tgjivcqgoojb5u

Using a novel fractional-order gradient method for CNN back-propagation [article]

Mundher Mohammed Taresh, Ningbo Zhu, Talal Ahmed Ali Ali, Mohammed Alghaili, Weihua Guo
2022 arXiv   pre-print
Therefore, the fractional-order gradient (FGD) method with a fixed memory step and an adjustable number of terms is used to update the weights of the layers.  ...  We also compared the performance of the developed fractional-order neural networks and Integer-order neural networks.  ...  Acknowledgments: This work was supported by the National Natural Science Foundation [61572177]. No additional external funding received for this study.  ... 
arXiv:2205.00581v1 fatcat:wjc4qosb7jcedjtnrt2wiqfqau

Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

Xia Huang, Zhen Wang, Yuxia Li
2013 Advances in Mathematical Physics  
A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are  ...  investigated.  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (nos. 61004078 and 61273012), China Postdoctoral Science Foundation funded project, and Special Funds for Postdoctoral  ... 
doi:10.1155/2013/657245 fatcat:eqswza2lm5bmdmjpr7egvsh6mm

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Jin-E Zhang
2017 Complexity  
In addition, we give some algebraic criteria for ascertaining the static multisynchronization of coupled fractional-order neural networks with fixed and switching topologies, respectively.  ...  We show that every subnetwork of a class of coupled fractional-order neural networks consisting of N identical subnetworks can have r+1n locally Mittag-Leffler stable equilibria.  ...  Acknowledgments The work is supported by the Research Project of Hubei Provincial Department of Education of China under Grant T201412.  ... 
doi:10.1155/2017/9323172 fatcat:jxw5xkjpfvahbdhj2wou2cic6a

An optimized fractional order PID controller for suppressing vibration of AC motor

Wu Deng, Huimin Zhao, Xinhua Yang, Xiumei Li, Chang Dong
2016 Journal of Vibroengineering  
So the Back Propagation (BP) neural network is selected to optimize the parameters of the fractional order PID controller in order to obtain the high performance.  ...  Then the optimized fractional order PID controller and the traditional PID controller are used to control AC motor speed governing system.  ...  Acknowledgements The authors would like to thank all the reviewers for their constructive comments. This research was supported by the National Natural Science Foundation of China (  ... 
doi:10.21595/jve.2016.16652 fatcat:nna3dq3sbresdc7es3rjni5psq

Synchronization Analysis of a Class of Neural Networks with Multiple Time Delays

Changyou Wang, Qiang Yang, Tao Jiang, Nan Li, Niansheng Tang
2021 Journal of Mathematics  
In this paper, we study the synchronization of a new fractional-order neural network with multiple delays.  ...  In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo  ...  [16] investigated the global projective synchronization of a fractional-order neural network and obtained some new criteria to realize projective synchronization of the fractional-order neural networks  ... 
doi:10.1155/2021/5573619 fatcat:wpkg3kelk5dtfc6wf6fjehk46e

Synchronization for a Class of Fractional-Order Neural Networks by Using State Feed-Back Control

Jin Xu, Xiulan Zhang, Hongxing Wang
2016 ICIC Express Letters  
This paper presents synchronization methods for a class of fractional-order neural networks by means of linear control.  ...  Of fundamental importance, the stability analysis for fractional-order neural networks in this paper can provide a framework for stability analysis in fractional-order systems.  ...  The authors are indebted to the anonymous reviewers' valuable comments, which improved the presentation and quality of this paper.  ... 
doi:10.24507/icicel.10.07.1741 fatcat:f6mq7aciune7vflvnvnjbl6ree

Complexity and Chimera States in a Ring-Coupled Fractional-Order Memristor Neural Network

Shaobo He
2020 Frontiers in Applied Mathematics and Statistics  
The dynamics of the fractional-order memristor neural model are investigated by means of bifurcation diagrams, Lyapunov exponents, and phase diagrams.  ...  In this paper, the fractional-order derivative is introduced into an improved memristor neural system.  ...  FORMATION AND DYNAMICS OF THE NEURAL NETWORK Formation of the Network The ring network of neural systems is investigated numerically. He et al.  ... 
doi:10.3389/fams.2020.00024 fatcat:7byb3zez75hk5jl6zmnbdz3bky

Mittag-Leffler stability analysis of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument

Liguang Wan, Ailong Wu
2017 Advances in Difference Equations  
The obtained criteria are useful in the analysis and design of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument.  ...  This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument.  ...  Authors' contributions All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.  ... 
doi:10.1186/s13662-017-1368-y fatcat:sea2ig4ddrhehafhixreimlbqa

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Hai Zhang, Renyu Ye, Jinde Cao, Ahmed Alsaedi
2017 Complexity  
This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses.  ...  on the order of fractional derivative and network parameters.  ...  Acknowledgments This work is jointly supported by the National Natural Science Fund of China (11301308, 61573096, and 61272530),  ... 
doi:10.1155/2017/6875874 fatcat:2zkim446abfs7psfjqi5oselxe

Artificial Neural Network Approach for Solving Fractional order initial value problems [article]

Susmita Mall, S. Chakraverty
2018 arXiv   pre-print
In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE).  ...  Combining the initial conditions with the ANN output gives us a suitable approximate solution of FDE.  ...  Acknowledgement The first author is thankful to Department of Science and Technology (DST), Government of India for financial support under Women Scientist Scheme-A.  ... 
arXiv:1810.04992v2 fatcat:u5qnvbqrprhjzmcvhln2kapdm4
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