Article
Computer Science, Interdisciplinary Applications
Ghada H. Ibraheem, Mustafa Turkyilmazoglu
Summary: In this work, the optimal variational iteration method was used to solve fractional differential equations, with an introduction of a parameter to accelerate convergence. The results showed that the proposed method exhibited better convergence and accuracy compared to the standard variational iteration method.
JOURNAL OF COMPUTATIONAL SCIENCE
(2022)
Article
Mathematics
Jing Chang, Jin Zhang, Ming Cai
Summary: In this paper, series solutions and approximate solutions of time-space fractional differential equations are obtained using two different analytical methods, namely the homotopy perturbation Sumudu transform method (HPSTM) and the variational iteration Laplace transform method (VILTM). It is found that the approximate solutions closely match the exact solutions. These solutions are significant for analyzing various phenomena and have not been reported in previous literature. The graphical presentations of the third approximate solutions for different values of order alpha are a notable feature of this work.
Article
Multidisciplinary Sciences
Rasool Shah, Azzh Saad Alshehry, Wajaree Weera
Summary: This paper introduces a new method called the variational iteration transformation method for solving nonlinear fractional-order gas dynamics equations. By applying the Shehu transformation and iterative technique, the proposed method does not require additional materials or computations. Testing on four problems demonstrates the accuracy and feasibility of this method.
Article
Mathematics, Applied
Yu-Ming Chu, Ehab Hussein Bani Hani, Essam R. El-Zahar, Abdelhalim Ebaid, Nehad Ali Shah
Summary: The article investigated fractional third-order dispersive partial differential equations using Shehu decomposition and variational iteration transform methods. Various fractional-order integral, derivative, and function were used as the basis of the methodology, with graphs and tables showing solution behavior. The comparison demonstrated the signed agreement of solutions and their accuracy, efficiency, and reliability were confirmed through numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Muhammad Naeem, Omar Fouad Azhar, Ahmed M. Zidan, Kamsing Nonlaopon, Rasool Shah
Summary: This research article introduces an innovative analytical technique for solving fractional-order parabolic equations, using the Adomian decomposition method and Elzaki transformation to obtain closed-form solutions. By plotting solution graphs and analyzing numerical examples, the effectiveness and accuracy of the method are demonstrated.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Computer Science, Interdisciplinary Applications
Fengying Zhou, Xiaoyong Xu
Summary: A new numerical method based on fractional-order hybrid functions and simulated annealing algorithm is proposed for solving fractional pantograph delay differential equations. The method simplifies the problem into algebraic equations using the properties and exact formulas of the hybrid functions, and solves them using Gaussian elimination and Picard iteration methods. The error analysis and optimization of the method are also investigated. Numerical examples verify the effectiveness and applicability of the proposed method.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Review
Mathematics, Interdisciplinary Applications
Jehad Alzabut, Ravi P. Agarwal, Said R. Grace, Jagan M. Jonnalagadda
Summary: This survey paper succinctly reviews the recent progress in the field of oscillation theory for linear and nonlinear fractional differential equations, providing a fundamental background for researchers interested in contributing to this topic.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Boonrod Yuttanan, Mohsen Razzaghi, Thieu N. Vo
Summary: This paper presents a numerical method for solving distributed-order fractional partial differential equations by introducing fractional-order generalized Taylor wavelets and studying the estimation of the approximation error. A formula for determining the Riemann-Liouville fractional integral operator for the wavelets is provided using the regularized beta function, and combined with Gauss-Legendre quadrature to obtain the numerical method. Several illustrative examples are given to demonstrate the applicability and accuracy of the proposed method.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ri Zhang, Nehad Ali Shah, Essam R. El-Zahar, Ali Akgul, Jae Dong Chung
Summary: This work introduces a new semi-analytical method, the variational iteration transform method, for investigating fractional-order Emden-Fowler equations. The Shehu transformation and the iterative method are utilized to solve the given problems. The proposed method demonstrates higher accuracy compared to other techniques and does not require additional calculations. Numerical problems validate the effectiveness of the suggested method in solving nonlinear fractional-order problems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohamed A. Abdelkawy, Ahmed Z. M. Amin, Antonio M. Lopes, Ishak Hashim, Mohammed M. Babatin
Summary: In this paper, a fractional-order shifted Jacobi-Gauss collocation method is proposed to solve variable-order fractional integro-differential equations with weakly singular kernel. By solving systems of algebraic equations, the approximate solutions of the equations are obtained using Riemann-Liouville fractional integral and derivative as well as fractional-order shifted Jacobi polynomials. The method demonstrates superior accuracy through numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Jiarong Zuo, Juan Yang
Summary: This paper provides the first rigorous proof that solutions of a class of fractional differential equations can be approximated by residual networks (ResNets) and there is an upper bound on the number of parameters of these ResNets. The proof is based on the variational iteration method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Hoa T. B. Ngo, Mohsen Razzaghi, Thieu N. Vo
Summary: In this paper, we propose an efficient numerical approach to solve variable-order fractional differential equations (VO-FDEs) using fractional-order generalized Chelyshkov wavelets (FOGCW). By using the beta function to determine the exact value for the Riemann-Liouville fractional integral operator of the FOGCW and applying it to solve the VO-FDEs, we demonstrate the effectiveness of this method through six examples. In the last example, we show the application of our method to the variable-order fractional relaxation model.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Multidisciplinary
Rashid Nawaz, Nasir Ali, Laiq Zada, Kottakkkaran Sooppy Nisar, M. R. Alharthi, Wasim Jamshed
Summary: This article introduces a new method known as the Natural Transform Iterative Method (NTIM) for solving fractional order differential equations, and compares its efficiency and consistency with the existing Natural Transform Decomposition Method (NTDM) using test examples. The results suggest that NTIM is more efficient and consistent than NTDM.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Multidisciplinary Sciences
Saima Noor, Ma'mon Abu Hammad, Rasool Shah, Albandari W. Alrowaily, Samir A. El-Tantawy
Summary: In this study, the fractional Fornberg-Whitham equation (FFWE) is solved and analyzed using the variational iteration method (VIM) and Adomian decomposition method (ADM) aided by the Aboodh transformation (AT). The FFWE is an important model for describing nonlinear wave propagations in various scientific fields and plasma physics. The AT is a powerful tool for transforming fractional-order differential equations (DEs) into integer-order ones, enabling analytical solutions. The main objective of this investigation is to demonstrate the effectiveness and accuracy of ADM and VIM in deriving approximations for the FFWE and to highlight their advantages and potential applications in solving other fractional-order nonlinear problems in scientific fields, particularly in plasma physics and engineering.
Article
Mathematics, Applied
Quan H. Do, Hoa T. B. Ngo, Mohsen Razzaghi
Summary: A new effective method utilizing fractional-order Chebyshev wavelets is presented for solving two-dimensional distributed-order fractional differential equations (DOFDEs). An exact formula involving regularized beta functions is provided to determine the Riemann-Liouville fractional integral operator of these wavelets. The method yields accurate results and is supported by numerical examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Computer Science, Software Engineering
Xinyi Yu, Hanxiong Li, Haidong Yang
Summary: This paper proposes an algorithm for low-light image enhancement that addresses the issues of noise and color distortion by integrating denoising and color restoration. Experimental results demonstrate that this method greatly improves the quality of low-light images.
Article
Computer Science, Artificial Intelligence
Qian-Qian Li, Zi-Peng Wang, Tingwen Huang, Huai-Ning Wu, Han-Xiong Li, Junfei Qiao
Summary: This article addresses fault-tolerant stochastic sampled-data fuzzy control for nonlinear delayed parabolic PDE systems under spatially point measurements. A T-S fuzzy PDE model is used to accurately describe the system. A fault-tolerant SD fuzzy controller with stochastic sampling is designed considering possible actuator failure, and a novel time-dependent Lyapunov functional is constructed to obtain sufficient conditions for the mean square exponential stability of the closed-loop system based on linear matrix inequalities. The effectiveness of the designed approach is illustrated through three examples.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
Peng Wei, Han-Xiong Li
Summary: In this article, a spatiotemporal entropy method is proposed to detect and locate thermal abnormalities of Li-ion battery (LIB) packs. The spatial entropy and temporal entropy are constructed from different scales based on Karhunen-Loeve (KL) decomposition, and then integrated into the comprehensive spatiotemporal entropy. The kernel density estimation is used to derive the detection threshold, and the entropy contribution function is designed for abnormality localization. Experimental results demonstrate the effectiveness of the proposed method in timely detecting and precisely locating abnormal cells at the early stage.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Lei Lei, Han-Xiong Li, Hai-Dong Yang
Summary: This article proposes a multiscale convolution-based detection methodology for classifying defects in bare printed circuit boards (PCBs) under uncertainty. A novel window-based loss function is designed to tackle inter-class imbalance and uncertainty. A multiscale convolution network is constructed to process defects with intra-class variance, and large scale extraction features are fused on the small scale to guide the extraction process. Experimental studies demonstrate that the proposed methodology achieves satisfactory detection performance and visual interpretability compared to baseline methods.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Engineering, Electrical & Electronic
Xinyi Yu, Han-Xiong Li, Haidong Yang
Summary: Surface defect detection of printed circuit boards (PCBs) is a critical stage in ensuring product quality. Existing defect detection methods using deep learning models are limited by image uncertainty and label uncertainty. This paper proposes a novel collaborative learning classification model that addresses these difficulties. Results show that the proposed model achieves excellent performance on various quantitative metrics.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Mathematics
Hu Wang, Sha Wang, Yajuan Gu, Yongguang Yu
Summary: This paper introduces a simplified two-dimensional Hodgkin-Huxley model that is exposed to electric fields. The study investigates the Hopf bifurcations of the simplified model through qualitative analysis and numerical simulations. The paper derives a necessary and sufficient condition for the existence of Hopf bifurcations and obtains the conditions for supercritical and subcritical Hopf bifurcations. Bifurcation diagrams are provided for two parameters, and numerical examples are used to demonstrate the efficacy of the theoretical results.
Article
Automation & Control Systems
Zhijia Zhao, Yiming Liu, Tao Zou, Keum-Shik Hong, Han-Xiong Li
Summary: In this study, a novel adaptive fault-tolerant control strategy is proposed to address the vibration issues in marine risers, ensuring system stability and performance.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jian Hou, Xiangyun Meng, Jingjia Wang, Yongsheng Han, Yongguang Yu
Summary: This paper considers the numerical method for a multiterm time-fractional reaction-diffusion equation with classical Robin boundary conditions. The full discrete scheme is constructed using the L1-finite difference method, which involves using the L1 scheme on graded meshes for temporal discretisation of each Caputo fractional derivative and the finite difference method on uniform meshes for spatial discretisation. By carefully dealing with the discretisation of Robin boundary conditions, sharp error analysis is proven at each time level. Additionally, numerical results that confirm the sharpness of the error estimates are presented.
FRACTAL AND FRACTIONAL
(2023)
Article
Automation & Control Systems
Xian-Bing Meng, C. L. Philip Chen, Han-Xiong Li
Summary: In industrial applications, the modeling and online applications of distributed parameter systems (DPSs) are difficult due to their infinite dimension, spatiotemporal coupled dynamics, nonlinearity, and model uncertainties. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. The proposed method integrates evolutionary learning-based spatial basis function, efficient broad learning system for temporal dynamics, and Gaussian process regression for spatiotemporal-scale learning to enable online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of the proposed method.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Automation & Control Systems
Zhijia Zhao, Yiming Liu, Ge Ma, Keum-Shik Hong, Han-Xiong Li
Summary: In this article, a new adaptive fuzzy fault-tolerant control (FTC) is proposed for a three-dimensional riser-vessel system with unknown backlash nonlinearity. A model for the smooth inverse dynamics of the backlash is introduced and the control input is divided into an expected input and a compensation error. Fuzzy adaptive technology is employed to achieve compensation considering the imprecision of system modeling and unknown external disturbances. The simulation results demonstrate the effectiveness of the derived scheme.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Automation & Control Systems
Zhijia Zhao, Yiming Liu, Sentao Cai, Zhifu Li, Yiwen Wang, Keum-Shik Hong, Han-Xiong Li
Summary: This article proposes an adaptive control method for a flexible manipulator to deal with distributed disturbances, unknown dead zones, and input quantization. The unknown dead zone and input quantization are formulated and represented based on essential transformations. An adaptive robust quantized control with online updating laws is developed to ensure robustness, angle position, and reduce vibration. The Lyapunov theoretical analysis is employed to ensure bounded stability. Numerical simulations and experiments are conducted to verify the feasibility and superiority of the proposed method using a Quanser platform.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics
Jun Xu, Wei Hu, Wenjuan Gu, Yongguang Yu
Summary: The study proposes an improved discrete JAYA algorithm, called QSA-DJAYA, based on reinforcement learning and simulated annealing, for solving the traveling salesman problem in combinatorial optimization. The algorithm embeds the Q-learning algorithm into JAYA algorithm to update the solution by selecting the most promising transformation operator. It also introduces the Metropolis acceptance criterion from simulated annealing to balance exploration and exploitation, and applies 3-opt at certain frequency to improve efficiency. Experimental results show that the QSA-DJAYA algorithm achieves significantly better results compared to other competitive algorithms in most instances.
Article
Computer Science, Artificial Intelligence
Yun Feng, Yaonan Wang, Yang Mo, Yiming Jiang, Zhijie Liu, Wei He, Han-Xiong Li
Summary: Fault detection for distributed parameter systems (DPSs) generally requires the complete model information to be known. However, it is common that accurate first-principles physical models are difficult to obtain for many industrial applications. Therefore, the applicability of traditional model-based methods is limited. In this study, an adaptive neural network (AdNN) is constructed to estimate the state variable and the unknown nonlinearity for a class of partially known nonlinear DPSs. Experimental results validate the effectiveness of the proposed method.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Engineering, Electrical & Electronic
Yaxin Wang, Han-Xiong Li, Shengli Xie
Summary: In this article, a spatial model predictive control (MPC) approach is proposed for a nonlinear distributed parameter system (DPS). A data-driven modeling method is utilized to predict the system performance, and a dual adaptation approach is developed to capture the most recent dynamics. Theoretical analysis guarantees stability, and simulations/experiments demonstrate the effectiveness of the proposed method.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Automation & Control Systems
Jinhui Zhou, Wenjing Shen, Zhengwei Ma, Xiaolin Mou, Yu Zhou, Han-Xiong Li, Liqun Chen
Summary: This article proposes a Chebyshev-Galerkin-based thermal fault detection and localization framework for the pouch-type Li-ion battery under limited sensing. The method utilizes Chebyshev functions to construct spatial basis functions and derives time coefficients through the Galerkin method. The proposed method demonstrates effectiveness in fault detection and localization through simulations and experiments.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
(2023)
Article
Physics, Multidisciplinary
Xiaoyu Shi, Jian Zhang, Xia Jiang, Juan Chen, Wei Hao, Bo Wang
Summary: This study presents a novel framework using offline reinforcement learning to improve energy consumption in road transportation. By leveraging real-world human driving trajectories, the proposed method achieves significant improvements in energy consumption. The offline learning approach demonstrates generalizability across different scenarios.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Junhyuk Woo, Soon Ho Kim, Hyeongmo Kim, Kyungreem Han
Summary: Reservoir computing (RC) is a new machine-learning framework that uses an abstract neural network model to process information from complex dynamical systems. This study investigates the neuronal and network dynamics of liquid state machines (LSMs) using numerical simulations and classification tasks. The findings suggest that the computational performance of LSMs is closely related to the dynamic range, with a larger dynamic range resulting in higher performance.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Yuwei Yang, Zhuoxuan Li, Jun Chen, Zhiyuan Liu, Jinde Cao
Summary: This paper proposes an extreme learning machine (ELM) algorithm based on residual correction and Tent chaos sequence (TRELM-DROP) for accurate prediction of traffic flow. The algorithm reduces the impact of randomness in traffic flow through the Tent chaos strategy and residual correction method, and avoids weight optimization using the iterative method. A DROP strategy is introduced to improve the algorithm's ability to predict traffic flow under varying conditions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Chengwei Dong, Min Yang, Lian Jia, Zirun Li
Summary: This work presents a novel three-dimensional system with multiple types of coexisting attractors, and investigates its dynamics using various methods. The mechanism of chaos emergence is explored, and the periodic orbits in the system are studied using the variational method. A symbolic coding method is successfully established to classify the short cycles. The flexibility and validity of the system are demonstrated through analogous circuit implementation. Various chaos-based applications are also presented to show the system's feasibility.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Viorel Badescu
Summary: This article discusses the maximum work extraction from confined particles energy, considering both reversible and irreversible processes. The results vary for different types of particles and conditions. The concept of exergy cannot be defined for particles that undergo spontaneous creation and annihilation. It is also noted that the Carnot efficiency is not applicable to the conversion of confined thermal radiation into work.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
P. M. Centres, D. J. Perez-Morelo, R. Guzman, L. Reinaudi, M. C. Gimenez
Summary: In this study, a phenomenological investigation of epidemic spread was conducted using a model of agent diffusion over a square region based on the SIR model. Two possible contagion mechanisms were considered, and it was observed that the number of secondary infections produced by an individual during its infectious period depended on various factors.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zuan Jin, Minghui Ma, Shidong Liang, Hongguang Yao
Summary: This study proposes a differential variable speed limit (DVSL) control strategy considering lane assignment, which sets dynamic speed limits for each lane to attract vehicle lane-changing behaviors before the bottleneck and reduce the impact of traffic capacity drop. Experimental results show that the proposed DVSL control strategy can alleviate traffic congestion and improve efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Matthew Dicks, Andrew Paskaramoorthy, Tim Gebbie
Summary: In this study, we investigate the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event-driven agent-based financial market model. The results show that the agents with smaller state spaces converge faster and are able to intuitively learn to trade using spread and volume states. The introduction of the learning agent has a robust impact on the moments of the model, except for the Hurst exponent, which decreases, and it can increase the micro-price volatility as trading volumes increase.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zhouzhou Yao, Xianyu Wu, Yang Yang, Ning Li
Summary: This paper developed a cooperative lane-changing decision system based on digital technology and indirect reciprocity. By introducing image scoring and a Q-learning based reinforcement learning algorithm, drivers can continuously evaluate gains and adjust their strategies. The study shows that this decision system can improve driver cooperation and traffic efficiency, achieving over 50% cooperation probability under any connected vehicles penetration and traffic density, and reaching 100% cooperation probability under high penetration and medium to high traffic density.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Josephine Nanyondo, Henry Kasumba
Summary: This paper presents a multi-class Aw-Rascle (AR) model with area occupancy expressed in terms of vehicle class proportions. The qualitative properties of the proposed equilibrium velocity and the stability conditions of the model are established. The numerical results show the effect of proportional densities on the flow of vehicle classes, indicating the realism of the proposed model.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Oliver Smirnov
Summary: This study proposes a new method for simultaneously estimating the parameters of the 2D Ising model. The method solves a constrained optimization problem, where the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. Monte Carlo simulations were conducted using models of different shapes and sizes to evaluate the performance of the method with and without the Hamiltonian constraint. The results demonstrate that the proposed estimation method yields lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Przemyslaw Chelminiak
Summary: The study investigates the first-passage properties of a non-linear diffusion equation with diffusivity dependent on the concentration/probability density through a power-law relationship. The survival probability and first-passage time distribution are determined based on the power-law exponent, and both exact and approximate expressions are derived, along with their asymptotic representations. The results pertain to diffusing particles that are either freely or harmonically trapped. The mean first-passage time is finite for the harmonically trapped particle, while it is divergent for the freely diffusing particle.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Hidemaro Suwa
Summary: The choice of transition kernel is crucial for the performance of the Markov chain Monte Carlo method. A one-parameter rejection control transition kernel is proposed, and it is shown that the rejection process plays a significant role in determining the sampling efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Xudong Wang, Yao Chen
Summary: This article investigates the joint influence of expanding medium and constant force on particle diffusion. By starting from the Langevin picture and introducing the effect of external force in two different ways, two models with different force terms are obtained. Detailed analysis and derivation yield the Fokker-Planck equations and moments for the two models. The sustained force behaves as a decoupled force, while the intermittent force changes the diffusion behavior with specific effects depending on the expanding rate of the medium.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
