Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example

Finite-time projective synchronization of fractional-order delayed quaternion-valued fuzzy memristive neural networks

In this paper, the finite-time projective synchronization (FTPS) problem of fractionalorder quaternion-valued fuzzy memristor neural networks (FOQVFMNNs) is studied. Through establishing a feedback controller with signed functions and an adaptive controller, sufficient conditions for FTPS for FOQVFMNNs are obtained. Furthermore, the synchronization establishment time is calculated. Finally, the practicability of the conclusions is verified by numerical simulations

Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays

This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes

Finite-time stabilization for fractional-order inertial neural networks with time varying delays

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results

An improved data classification framework based on fractional particle swarm optimization

Particle Swarm Optimization (PSO) is a population based stochastic optimization technique which consist of particles that move collectively in iterations to search for the most optimum solutions. However, conventional PSO is prone to lack of convergence and even stagnation in complex high dimensional-search problems with multiple local optima. Therefore, this research proposed an improved Mutually-Optimized Fractional PSO (MOFPSO) algorithm based on fractional derivatives and small step lengths to ensure convergence to global optima by supplying a fine balance between exploration and exploitation. The proposed algorithm is tested and verified for optimization performance comparison on ten benchmark functions against six existing established algorithms in terms of Mean of Error and Standard Deviation values. The proposed MOFPSO algorithm demonstrated lowest Mean of Error values during the optimization on all benchmark functions through all 30 runs (Ackley = 0.2, Rosenbrock = 0.2, Bohachevsky = 9.36E-06, Easom = -0.95, Griewank = 0.01, Rastrigin = 2.5E-03, Schaffer = 1.31E-06, Schwefel 1.2 = 3.2E-05, Sphere = 8.36E-03, Step = 0). Furthermore, the proposed MOFPSO algorithm is hybridized with Back-Propagation (BP), Elman Recurrent Neural Networks (RNN) and Levenberg-Marquardt (LM) Artificial Neural Networks (ANNs) to propose an enhanced data classification framework, especially for data classification applications. The proposed classification framework is then evaluated for classification accuracy, computational time and Mean Squared Error on five benchmark datasets against seven existing techniques. It can be concluded from the simulation results that the proposed MOFPSO-ERNN classification algorithm demonstrated good classification performance in terms of classification accuracy (Breast Cancer = 99.01%, EEG = 99.99%, PIMA Indian Diabetes = 99.37%, Iris = 99.6%, Thyroid = 99.88%) as compared to the existing hybrid classification techniques. Hence, the proposed technique can be employed to improve the overall classification accuracy and reduce the computational time in data classification applications

A computational fractional order model for optimal control of wearable healthcare monitoring devices for maternal health

The post-COVID-19 landscape has propelled the global telemedicine sector to a projected valuation of USD 91.2 billion by 2022, with a remarkable compounded annual growth rate (CAGR) of 18.6% from 2023 to 2030. This paper introduces an analytical wearable healthcare monitoring device (WHMD) designed for the timely detection and seamless transmission of crucial health vitals to telemedical cloud agents. The fractional order modeling approach is employed to delineate the efficacy of the WHMD in pregnancy-related contexts. The Caputo fractional calculus framework is harnessed to show the device potential in capturing and communicating vital health data to medical experts precisely at the cloud layer. Our formulation establishes the fractional order model's positivity, existence, and uniqueness, substantiating its mathematical validity. The investigation comprises two major equilibrium points: the disease-free equilibrium and the equilibrium accounting for disease presence, both interconnected with the WHMD. The paper explores the impact of integrating the WHMD during pregnancy cycles. Analytical findings show that the basic reproduction number remains below unity, showing the WHMD efficacy in mitigating health complications. Furthermore, the fractional multi-stage differential transform method (FMSDTM) facilitates optimal control scenarios involving WHMD utilisation among pregnant patients. The proposed approach exhibits robustness and conclusively elucidates the dynamic potential of WHMD in supporting maternal health and disease control throughout pregnancy. This paper significantly contributes to the evolving landscape of analytical wearable healthcare research, highlighting the critical role of WHMDs in safeguarding maternal well-being and mitigating disease risks in edge reconfigurable health architectures

Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks

© 2020 Elsevier Inc. This paper proposes two methods to investigate the problem of finite-time Mittag-Leffler synchronization for the systems of fractional-order quaternion-valued neural networks (FQVNNs) with two kinds of activation functions, respectively. Generally, the first method mainly reflects in the new establishment of Lyapunov-Krasovskii functionals (LKFs) and the novel application of a new fractional-order derivative inequality which contains and exploits the wider coefficients with more values. Meanwhile, the second one is embodied in the comprehensive development of both the norm comparison rules and the generalized Gronwall-Bellman inequality with the help of Laplace transform of Mittag-Leffler function. Thanks to the above two methods, the flexible synchronization criteria are easily and separately obtained for the studied four systems of FQVNNs with general activation functions and linear threshold ones. Finally, two numerical simulations are given to demonstrate the feasibility and effectiveness of the newly proposed approaches

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal