Article
Mathematics, Interdisciplinary Applications
Arran Fernandez, Hafiz Muhammad Fahad
Summary: We conducted a formal study on weighted fractional calculus and its extension, comparing it with classical Riemann-Liouville fractional calculus, proving fundamental properties and solving ordinary differential equations in specific cases.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Electrical & Electronic
Xuejiao Zhao, Shipeng Wang, Qiong Wu, Yanju Ji
Summary: The theory of magnetic-source electromagnetic anomalous diffusion is developed, presenting a multiscale electromagnetic anomalous diffusion theory with improved generalized electrical conductivity. This theory is applied to propose a 3-D modeling method for complex electromagnetic propagation in rough geologic medium, demonstrating improved efficiency and accuracy in detection.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Article
Engineering, Mechanical
Li Ma, Bowen Wu
Summary: The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). The criteria of finite-time stability for linear and nonlinear HFDEs are established using the method of successive approximation and Beesack inequality with weakly singular kernel. A novel fractional delayed matrix function is given for linear HFDEs with pure delay, and both Beesack inequality and Holder inequality are utilized for nonlinear HFDEs with constant time delay. Several simulations are implemented to verify the effectiveness and practicability of the main results.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Erdem Ilten
Summary: This paper focuses on the design of a robust speed controller for a nonlinear system using fractional-order modeling. The fractional calculus is employed to model the system and a mixed sensitivity problem is formulated with fractional-order weighting functions. Experimental results confirm that the designed controller performs well in terms of tracking dynamics, robustness against load disturbances, and noise suppression.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Marine
Shiquan Zhao, Sizhe Wang, Ricardo Cajo, Weijie Ren, Bing Li
Summary: A nonlinear model predictive control method with fractional order cost functions is proposed for the marine boiler-turbine system to improve control performance. Experimental results show the superiority of this method compared to traditional methods.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, AliReza Bagheri Salec, Alaa Salim Jebur
Summary: This paper investigates a time fractional distributed-order diffusion equation and analyzes its stability, convergence, and numerical accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jean-Claude Trigeassou, Nezha Maamri
Summary: The paper introduces a new approach to fractional optimal control based on a frequency distributed representation of fractional differential equations combined with an original formulation of fractional energy to truly control the internal system state. By revisiting the fractional calculus of variations to express appropriate Euler Lagrange equations, the quadratic optimal control of fractional linear systems is formulated. Through a frequency discretization technique, theoretical equations are converted into an equivalent large dimension integer order system for the implementation of a feasible optimal solution, as demonstrated in a numerical example.
FRACTAL AND FRACTIONAL
(2021)
Article
Computer Science, Interdisciplinary Applications
Hai Zhang, Yuhong Cheng, Weiwei Zhang, Hongmei Zhang
Summary: This paper focuses on studying the quasi-uniform synchronization on fractional-order fuzzy neural networks with the proportional and distributed delays. The impacts of the Caputo derivative order, coefficients of network system and control gain constants on the synchronization performance are taken into account. Novel time-dependent and Caputo derivative order-dependent algebraic criteria on the quasi-uniform synchronization of FOFNNs are established, revealing the internal influences of the time and fractional derivative order on quasi-uniform synchronization.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Ali Habibirad, Esmail Hesameddini, Hadis Azin, Mohammad Hossein Heydari
Summary: Distributed-order fractional calculus is a rapidly growing field within the broader area of fractional calculus, with significant applications in designing complex systems. This study utilizes the direct meshless local Petrov-Galerkin (DMLPG) technique to numerically solve the distributed-order time fractional Cable equation. The DMLPG method discretizes the equation in space variables using a generalized moving least square (GMLS) process, allowing for a more cost-effective integration compared to polynomial methods. The stability and convergence rate of the time-discrete technique are also demonstrated, and the problem is transformed into a system of linear algebraic equations.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics
Muhammad Imran Liaqat, Eric Okyere
Summary: The article introduces the Laplace residual power series method (LRPSM) as an effective approach for solving fractional-order differential equations. It applies LRPSM to find analytical approximate and exact solutions of the time-fractional Black-Scholes option pricing equations (BSOPE) in the sense of the Caputo derivative. The method combines Laplace transform and residual power series method, requiring minimal computation for coefficient determination, and shows strong agreement with other series solution methods.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ting-Ting Song, Guo-Cheng Wu, Jia-Li Wei
Summary: This study introduces a Hadamard fractional sum based on the time-scale theory and defines h-fractional difference. It proves fundamental theorems and presents initial value problems of fractional difference equations, providing their equivalent fractional sum equations. It also derives the discrete Mittag-Leffler function solutions for linear fractional difference equations. The study concludes that the new discrete fractional calculus of Hadamard type is well defined.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Yeliang Xiao, Ahsan Fareed Shah, Tariq Javed Zia, Ebenezer Bonyah
Summary: The paper discusses generalize midpoint type inequalities for MT-convex functions in the setting of weighted fractional integral, showing that the results are more generalized than existing literature and many can be obtained immediately.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Computer Science, Artificial Intelligence
Taizhi Lv, Lian Tong, Jun Zhang, Yong Chen
Summary: The proposed method is a real-time physiological signal acquisition and analysis method based on fractional calculus and stream computing. It estimates physiological status using a fractal index, calculated by distributed parallel computing on a stream computing platform. Experimental results show its ability to distinguish heart health status and reflect driver mental status.
Article
Mathematics
Ardak Kashkynbayev, Fathalla A. Rihan
Summary: This paper investigates the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. The study focuses on the local and global stability of steady-states, deducing the basic reproductive threshold parameter. The effectiveness of the theoretical results is illustrated through the consideration of a Holling type III response function in numerical simulations.
Article
Mathematics
Masahiro Yamamoto
Summary: In this study, a framework based on operator theory in fractional Sobolev spaces is constructed to deal with fractional derivatives and time-fractional differential equations. This framework provides a feasible extension of the classical Caputo and the Riemann-Liouville derivatives within Sobolev spaces of fractional orders, including negative ones. It allows for a unified treatment of fractional calculus and time-fractional differential equations.
Article
Automation & Control Systems
Qi Zhang, Yunlong Shang, Yan Li, Naxin Cui, Bin Duan, Chenghui Zhang
Article
Chemistry, Physical
Yue Sun, Yan Li, Meijuan Yu, Zhongkai Zhou, Qi Zhang, Bin Duan, Yunlong Shang, Chenghui Zhang
JOURNAL OF POWER SOURCES
(2020)
Article
Microbiology
Yingnan Han, Ya Li, Zhekai Hu, Xiao Wang, Junze Liu, Xue Ren, Yanbo Yu, Yan Li, Wenjuan Li, Yundong Sun
Article
Food Science & Technology
Ya Li, Wen Li, Xiao Wang, Chao Ding, Junze Liu, Yan Li, Wenjuan Li, Yundong Sun
MOLECULAR NUTRITION & FOOD RESEARCH
(2020)
Article
Energy & Fuels
Zhang Qi, Cui Naxin, Li Yan, Duan Bin, Zhang Chenghui
JOURNAL OF ENERGY STORAGE
(2020)
Article
Multidisciplinary Sciences
Meijuan Yu, Yan Li, Igor Podlubny, Fengjun Gong, Yue Sun, Qi Zhang, Yunlong Shang, Bin Duan, Chenghui Zhang
JOURNAL OF ADVANCED RESEARCH
(2020)
Article
Energy & Fuels
Shizhong Li, Yan Li, Daduan Zhao, Chenghui Zhang
JOURNAL OF ENERGY STORAGE
(2020)
Article
Engineering, Electrical & Electronic
Daduan Zhao, Chenghui Zhang, Yue Sun, Shizhong Li, Bo Sun, Yan Li
Summary: This paper introduces two novel distributed secondary control protocols aimed at improving the power quality of AC islanded microgrids. The algorithms achieve faster convergence speeds through the event-triggered strategy, while ensuring that the event-triggered parameters are limited within a certain range.
IEEE TRANSACTIONS ON SMART GRID
(2021)
Article
Computer Science, Information Systems
Mazin Mohammed Mogadem, Yan Li, Daniel Limenew Meheretie
Summary: In today's world, the demand for security is crucial, especially with the rapid development of emerging technologies like IoE and IoT devices, emphasizing security is essential to drive environmental innovation. It is necessary to focus on the security of new technologies to avoid potential disastrous consequences, especially in the 5G era. Security issues are not only about technological development but also closely related to future research opportunities and achieving better strategies.
CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS
(2022)
Article
Green & Sustainable Science & Technology
Mazin Mohammed Mogadem, Yan Li
Summary: The design of mathematical models is based on conservation laws and the fundamental principles of modeling to address challenges in different working conditions and environments. Introducing memristive elements can satisfy these fundamental principles and goals of modeling.
Article
Automation & Control Systems
Daduan Zhao, Yan Li, Shizhong Li, Zhengran Cao, Chenghui Zhang
Summary: This article introduces a distributed event-triggered impulsive control strategy for addressing the constraints of communication channel resources and control energies in real networks, aiming to solve the consensus problem in multiagent networks. Moreover, sufficient conditions for consensus and the existence of Zeno-behavior are discussed, along with the quantitative relationship between fractional order parameters and event-triggered impulsive instants.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2022)
Article
Automation & Control Systems
Daduan Zhao, Chenghui Zhang, Xiangyang Cao, Chao Peng, Bo Sun, Ke Li, Yan Li
Summary: This article proposes a novel optimal energy management strategy using the distributed consensus-based ADMM algorithm and the differential privacy scheme to address the privacy leakage issue in distributed energy management.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
(2023)
Article
Engineering, Electrical & Electronic
Zhongkai Zhou, Yan Li, Qing-Guo Wang, Jinpeng Yu
Summary: In this article, a parameter identification method for an EIS-based model is proposed using geometric analysis. By fitting the impedance spectrum at intermediate frequencies with two depressed semicircles, the parameters of the EIS-based model are directly calculated, greatly reducing the computational complexity. The relationship between six model parameters identified based on EIS at different temperatures, states of charge (SoCs), and aging cycles, and capacity decay is analyzed. The results show that the charge transfer (CT) resistance always has an excellent linear correlation with capacity decay, and can be used as a health indicator for batteries.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Proceedings Paper
Automation & Control Systems
Shizhong Li, Yan Li, Yue Sun, Daduan Zhao, Chenghui Zhang
PROCEEDINGS OF 2020 IEEE 9TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE (DDCLS'20)
(2020)
Proceedings Paper
Automation & Control Systems
Fengjun Gong, Yan Li, Daduan Zhao, Lingzhi Zhang
PROCEEDINGS OF 2020 IEEE 9TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE (DDCLS'20)
(2020)
