Article
Engineering, Multidisciplinary
Hegui Zhu, Chong Liu, Wen-Ze Wu, Wanli Xie, Tongfei Lao
Summary: This study proposes a weakened fractional-order accumulation operator to alleviate the ill-condition of discrete grey system models and improve grey system theory. The weakened fractional-order accumulation operator, composed of an improved fractional-order accumulation operator and multiplicative transformation, reduces differences between elements in the coefficient matrix and enhances prediction performance. The findings demonstrate the effectiveness of the weakened fractional-order accumulation operator.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Computer Science, Artificial Intelligence
Honglin Yang, Mingyun Gao, Qinzi Xiao
Summary: This study proposes a generalized fractional-order accumulation grey power model for forecasting the demand of the home-appliance supply chain in China. The feasibility and effectiveness of the model are demonstrated through parameter estimation, error analysis, and time response function solution.
Article
Mathematics
Jun Zhang, Yanping Qin, Xinyu Zhang, Bing Wang, Dongxue Su, Huaqiong Duo
Summary: This study analyzed the classic NGM (1, 1, k) model and proposed the fractional order accumulation NGM (1, 1, k) model based on the optimal background value. The parameters of the proposed model were estimated using the particle swarm optimization algorithm, and empirical analysis was conducted on two actual cases with economic significance. The simulation and prediction results demonstrated the practicality and efficiency of the proposed FBNGM (1, 1, k) model, expanding the application scope of grey prediction models.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Zhengpeng Wu, Jianke Chen, Jianping Chai, Fangyuan Zhang
Summary: A new Grey model of complex accumulation is proposed in this paper, extending the parameter selection from the real axis to the complex plane. By introducing Lie group theory, new tools are provided for grey system and better simulation and prediction results are achieved.
JOURNAL OF GREY SYSTEM
(2021)
Article
Mathematics, Interdisciplinary Applications
Pshtiwan Othman Mohammed, Ohud Almutairi, Ravi P. Agarwal, Y. S. Hamed
Summary: This article focuses on analyzing the positivity, monotonicity and convexity of discrete nabla fractional operators with exponential kernels from the perspective of Riemann and Caputo operators. These operators are named discrete nabla Caputo-Fabrizio-Riemann and Caputo-Fabrizio-Caputo fractional operators. Furthermore, the article presents illustrative examples of the main lemmas in the case of Riemann-Liouville.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Christopher S. Goodrich, Jagan M. Jonnalagadda, Benjamin Lyons
Summary: We investigate positivity, monotonicity, and convexity results for discrete fractional operators with exponential kernels. Our findings reveal both similarities and dissimilarities between the exponential kernel case and fractional differences with other types of kernels, indicating that the qualitative information gleaned in the exponential kernel case is not precisely the same as in other cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Peng Huang, Jixiong Zhang, Ntigurirwa Jean Damascene, Chaowei Dong, Zhaojun Wang
Summary: An innovative initial damage coal sample test method was proposed to study the impact of initial damage on the creep characteristics of coal samples. The study found that with the increase of initial damage, the creep time of coal samples shortened and the rate of accelerated creep damage increased sharply. The established fractional viscosity coefficient relationship and improved creep model in the acceleration phase provided a better description of the creep characteristics of coal samples with initial damage.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Multidisciplinary Sciences
Ting Jin, Shangce Gao, Hongxuan Xia, Hui Ding
Summary: This study presents a competing failure model for reliability analysis of a fractional-order RC circuit system, demonstrating its practical importance through numerical simulations.
JOURNAL OF ADVANCED RESEARCH
(2021)
Article
Mathematics, Applied
Pshtiwan Othman Mohammed, Christopher S. Goodrich, Faraidun Kadir Hamasalh, Artion Kashuri, Y. S. Hamed
Summary: In this study, we investigate the conditions under which the positivity of a fractional difference implies positivity, monotonicity, or convexity in both non-sequential and sequential cases. We focus on the discrete nabla ABC-type difference, which has a Mittag-Leffler kernel, leading to different results compared to other kernel types. Lastly, we apply our findings to certain classes of initial value problems in discrete fractional calculus.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Yiheng Wei, Nan Su, Linlin Zhao, Jinde Cao
Summary: This paper investigates the stability of linear time invariant delay delta fractional order systems. A sector region is constructed based on the analysis of the stable region, which serves as a proper subset. A variable is introduced to control the angle of the sector region, enhancing the flexibility. Additionally, the equivalent LMI condition corresponding to the sector region is developed, and the method is applied in controller design.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Mechanical
Wenli Xie, Chunhua Wang, Hairong Lin
Summary: Fractional-order calculus is used to develop a memristor with multistable locally active characteristics, showing stronger memory properties than integer-order memristors. This memristor is then applied in a chaotic system, resulting in new phenomena such as transient transitions and state jumps. Circuit simulations confirm the validity of the numerical results.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
T. Jakubowski, G. Serafin
Summary: This paper considers the existence of solutions for the fractional Burgers equation with a large class of initial conditions. It applies the results to a specific initial condition and investigates the properties of the selfsimilar solution.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Engineering, Mechanical
Zhou Fengyu, Wang Yugang
Summary: This study applies closed-loop D-alpha-type iterative learning control with a proportional D-type updating law to address initial shift in nonlinear conformable fractional order systems. Frameworks for fractional order ILC experiencing initial shift problem in path tracking are discussed. Sufficient condition for convergence of tracking errors in time domain is obtained by introducing -norm and Holder's inequality. Numerical examples demonstrate effectiveness of the proposed methods.
NONLINEAR DYNAMICS
(2021)
Article
Thermodynamics
Zekai Li, Xi Hu, Huan Guo, Xin Xiong
Summary: This paper proposes a novel WAWBO-FSGGM(1,1) model based on weighted average weakening buffer operator for accurate prediction of hydropower generation. The model utilizes seasonal data grouping, the WAWBO method, and fractional accumulated generating operation. The Whale Optimization Algorithm is used to optimize the model parameters and improve the predictive accuracy, as demonstrated by empirical results.
Article
Automation & Control Systems
Zhang Zhe, Toshimitsu Ushio, Zhang Jing, Wang Yaonan
Summary: This paper proposes a novel stability condition for distributed order composite systems with delay based on properties of Caputo fractional-order derivatives and a new method of vector Lyapunov function combined with M-matrix. The paper extends the properties of Caputo fractional-order derivatives to their distributed order form and introduces a new method to solve the stability problem of distributed order systems. The authors also address the stability problem of distributed order composite systems with time-delay and provide numerical simulation examples to validate the proposed stability condition.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Lifeng Wu, Sifeng Liu, Yingjie Yang
APPLIED SOFT COMPUTING
(2016)
Article
Geosciences, Multidisciplinary
Lifeng Wu, Xiaohui Gao, Yanli Xiao, Sifeng Liu, Yingjie Yang
Article
Engineering, Multidisciplinary
Chong Li, Yingjie Yang, Sifeng Liu
APPLIED MATHEMATICAL MODELLING
(2019)
Article
Computer Science, Interdisciplinary Applications
Wenjie Dong, Sifeng Liu, Yangyang Du
COMPUTERS & INDUSTRIAL ENGINEERING
(2019)
Article
Computer Science, Interdisciplinary Applications
Huan Wang, Zhigeng Fang, Daao Wang, Sifeng Liu
COMPUTERS & INDUSTRIAL ENGINEERING
(2020)
Article
Automation & Control Systems
Saad Ahmed Javed, Amin Mahmoudi, Sifeng Liu
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
(2020)
Article
Computer Science, Information Systems
Zhao Wang, Sifeng Liu, Zhigeng Fang
IEEE SYSTEMS JOURNAL
(2020)
Article
Environmental Sciences
Xiaorui Guo, Lifeng Wu, Meng Wang
Summary: With the proposal of China's high-quality development strategy, the coordinated and stable development of the Beijing-Tianjin-Hebei region has become a focus of research. Through model analysis, it is found that there is not obvious coordination among the three regions and they have not yet reached a state of mutual promotion. Therefore, four suggestions are put forward to promote coordinated development.
INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH
(2022)
Article
Environmental Sciences
Lifeng Wu, Yuan Meng
Summary: Since the implementation of the sustainable development strategy, China has made great efforts to save water resources. Effective prediction and analysis of regional water consumption are crucial for the regional economy. The DGMC(1,2) model is proposed for forecasting water requirements in five provinces in North China, considering the three industries and population. The results show that the DGMC(1,2) model is an efficient method for predicting water requirements, and the interval DGMC(1,2) model is used for predicting the range of water requirements. The analysis of water requirement trends in each region provides practical value and can be used for policy-making.
Article
Mathematics, Interdisciplinary Applications
Yunfei Yang, Jiamei Xiong, Lei Zhao, Xiaomei Wang, Lianlian Hua, Lifeng Wu
Summary: Cryptocurrency prices are highly volatile, making it difficult to predict their prices. This study proposes a novel prediction method, using a fractional grey model (FGM (1,1)), to predict the price of blockchain cryptocurrency. The research results show that the FGM (1,1) achieves a highly accurate level of prediction for the closing prices of BTC, ETH, and LTC, outperforming the GM (1,1) in terms of predictive capability. This study provides a feasible new method for price prediction and has practical implications for government departments, investors, and researchers.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Artificial Intelligence
Ningning Lu, Sifeng Liu, Junliang Du, Zhigeng Fang, Wenjie Dong, Liangyan Tao, Yingjie Yang
Summary: It is important to detect internal operating regularity in system developing with poor information. A grey relational analysis (GRA) method is proposed to identify the real relationship among multi factors, considering the changes of fluctuating sequences. The proposed GRA model can effectively identify the relationship and has small time-delay impact.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Yuhan Xie, Yunfei Yang, Lifeng Wu
Summary: This paper uses the gray relational analysis model to study the relationship between power consumption indicators of the three major industries in China and some social and economic indicators, and establishes a forecasting model for electricity consumption in these industries. The results indicate that the tertiary and secondary industries have the highest electricity consumption, and it is estimated that the power consumption of the three major industries in China will reach 10.15 trillion kWh by 2030.
Article
Economics
Amin Mahmoudi, Saad Ahmed Javed, Sifeng Liu, Xiaopeng Deng
TECHNOLOGICAL AND ECONOMIC DEVELOPMENT OF ECONOMY
(2020)
Proceedings Paper
Business, Finance
Bin Fu, Lifeng Wu
PROCEEDINGS OF 2017 IEEE INTERNATIONAL CONFERENCE ON GREY SYSTEMS AND INTELLIGENT SERVICES (GSIS)
(2017)
Article
Mathematics, Interdisciplinary Applications
Xiaojun Guo, Sifeng Liu, Yingjie Yang, Lifeng Wu
JOURNAL OF GREY SYSTEM
(2017)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
