Article
Mathematics
Xinfeng Zhang, Xiangjun Li, Kaikai Yang, Zhongyi Wang
Summary: This study proposes a fractional-order impedance model (FOIM) to characterize the dynamic properties of the internal behavior of lithium-ion batteries using fractional-order elements. The fractional-order extended Kalman filter (FEKF) algorithm is introduced to predict the battery charge state, considering the highly nonlinear characteristics of lithium-ion batteries. Comparative analysis of simulation and experimental results shows that the FOIM has significantly improved accuracy compared to equivalent circuit models (ECMs), and the FEKF algorithm has good robustness in estimating the state of charge (SOC) of the battery.
Article
Multidisciplinary Sciences
Yanli Qi, Gang Tian, Mingzhou Bai, Linlin Song
Summary: This article studies the prediction of deformations and disaster warnings during karst slope construction. It proposes an improved cusp mutation model and analyzes the deformation trend and sudden change types. By using virtual reality-mutation model and gray prediction model, the critical control warning value for slope deformation is obtained, providing a basis for risk evaluation.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Interdisciplinary Applications
Harendra Singh, Dumitru Baleanu, Jagdev Singh, Hemen Dutta
Summary: The study examines a non-integer order smoking model using an iterative scheme, discussing the stability of the model and the efficiency of the iterative scheme used. The proposed technique is found to have high accuracy and low computational cost, with figures showing the fractional time behavior of the solution.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Claudia A. Perez-Pinacho, Cristina Verde
Summary: This study addresses the problem of equivalence between fractional and integer order diffusion models, and proves the existence of a unique integral transformation mapping the solution of the integer order model to a solution of the fractional order model. The corresponding inverse integral transformation is established to guarantee the equivalence and well-posedness of the solutions of these models. Finally, the proposed method is compared with the Fourier transform method through a specific example, demonstrating its effectiveness.
Review
Mathematics, Interdisciplinary Applications
Kishore Bingi, B. Rajanarayan Prusty, Abhaya Pal Singh
Summary: Robot manipulators are widely used in various fields and are crucial for future complex infrastructures in space. They are also valuable in places where it is unsafe for humans, such as deep-sea exploration and radioactive environments. However, the time-varying constraints and uncertainties of robotic manipulators pose challenges in their modeling and control.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics
Vasily E. Tarasov
Summary: An extension of the general fractional calculus (GFC) proposed by Luchko is formulated in this article. This extension is based on a multi-kernel approach using Laplace convolutions of different Sonin kernels. The article also considers the multi-kernel GFC of an arbitrary order in the case of intervals (a, b) where -infinity < a < b <= infinity. Examples of multi-kernel general fractional operators of arbitrary orders are proposed in this study.
Article
Mathematics, Applied
Ricardo Almeida
Summary: The aim of this work is to study various problems in the calculus of variations with a generalized fractional derivative governing the dynamics of the state function. The study includes the Euler-Lagrange equation, problems with integral and holonomic constraints, higher order derivatives, and the Herglotz variational problem.
Article
Mathematics, Interdisciplinary Applications
Chunna Zhao, Licai Dai, Yaqun Huang
Summary: This paper proposes a fractional order sequential minimal optimization (FOSMO) method based on the SMO algorithm and fractional order calculus, which can more accurately describe the actual system and obtain more accurate results. Firstly, the objective function is expressed by a fractional order function using the FOSMO method. Then, the representation and meaning of fractional order terms in the objective function are studied. Lastly, the objective function is optimized based on fractional order Lagrange multipliers, and experiments are conducted on linear and nonlinear classification cases. Experimental results show that the FOSMO method can achieve higher accuracy than the normal SMO method.
FRACTAL AND FRACTIONAL
(2023)
Article
Chemistry, Analytical
Dominik Sierociuk, Michal Macias
Summary: This paper presents a method for states, parameters, and fractional order estimation using Fractional Unscented Kalman Filter. The proposed method can be seen as a convenient tool for estimating and analyzing various dynamical systems with fractional constants or variable order nature.
Article
Computer Science, Information Systems
Yi Liu, Ping Li, Boqing Feng, Zeyu Wang, Xiaolei Xu, Congxu Li, Hanming Jing
Summary: This paper presents a detailed fractional order statistical theory to capture the key deformation feature and achieve active warning of railway infrastructure. The non-Gaussian features hidden in the monitored time series are revealed using α-stable distribution. Long-range correlation and multifractal properties are extracted using the fractional order statistical method. A novel fractional Bi-long short term memory model (F-BiLSTM) is used to predict the deformation of railway infrastructure, with superior prediction performances.
Article
Engineering, Electrical & Electronic
Lulu Cai, Fei Wu, Dongge Lei
Summary: This paper proposes a new method based on fractional gray model to predict asphalt pavement performance with higher accuracy compared to traditional models. The method utilizes fractional accumulating generating operation (FAGO) and differential evolution algorithm to improve prediction accuracy.
IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Prashant M. Gade, Sachin Bhalekar
Summary: This study investigates the stability of linear fractional order maps and finds that the evolution in the stable region is described by Mittag-Leffler functions with a well-defined effective Lyapunov exponent. The research also explores coupled linear fractional maps and stability at fixed points of fractional nonlinear maps, providing insights into the relationship between stability and eigenvalues of coefficient matrices.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Ivo Petras
Summary: This paper discusses new oscillator structures that include new elements called memory elements, such as memristors, meminductors, and memcapacitors. These circuits can exhibit oscillations and chaotic behavior, and new mathematical models for fractional-order elements and whole oscillator circuits are proposed.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Artificial Intelligence
Raafat Shalaby, Mohammad El-Hossainy, Belal Abo-Zalam, Tarek A. Mahmoud
Summary: In this paper, an online optimization approach of a fractional-order PID controller based on a fractional-order actor-critic algorithm (FOPID-FOAC) is proposed to improve the performance of nonlinear systems. The effectiveness of the proposed approach is proven by extensive simulations and compared against other control algorithms.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Hussam Alrabaiah, Anwar Zeb, Ebraheem Alzahrani, Kamal Shah
Summary: The study focuses on converting an existing tobacco smoking model to a fractional order, analyzing the application of fractional derivatives and investigating the positivity, boundness, and dynamics of the proposed model. Numerical results are obtained using the generalized Adams-Bashforth-Moulton Method (GABMM) and fourth-order Runge-Kutta (RK4) method in Matlab environment.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Environmental Sciences
L. Z. Wu, S. H. Li, M. Zhang, L. M. Zhang
ENVIRONMENTAL EARTH SCIENCES
(2019)
Article
Computer Science, Interdisciplinary Applications
L. Z. Wu, S. H. Li, R. Q. Huang, S. Y. Wang
ENGINEERING WITH COMPUTERS
(2020)
Article
Engineering, Geological
S. H. Li, L. Z. Wu, J. J. Chen, R. Q. Huang
Article
Mechanics
L. Z. Wu, X. H. Luo, S. H. Li
Summary: The study focuses on the role of creep in rock engineering safety and the development of a mathematical model to represent rock creep behaviors. Shear creep tests were conducted on mudstone specimens using a shear rheometer, and a new variable-parameter fractional derivative element-based model was proposed to accurately characterize the two stages of the rock creep process. The results showed that derivative orders have the greatest effect on shear creep.
MECHANICS OF TIME-DEPENDENT MATERIALS
(2021)
Article
Computer Science, Artificial Intelligence
L. Z. Wu, S. H. Li, R. Q. Huang, Q. Xu
APPLIED SOFT COMPUTING
(2020)
Article
Automation & Control Systems
S. H. Li, L. Z. Wu, X. H. Luo
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2020)
Article
Computer Science, Artificial Intelligence
S. H. Li, L. Z. Wu, Jinsong Huang
Summary: A novel model for predicting landslide displacement, FKGM, was proposed in this paper by combining fractional modeling, kernel function methods, and grey models. The application of FKGM in a case study of a landslide in Hubei, China, showed that it can reliably predict large deformation of landslides. The results indicate that FKGM outperforms LSSVM and the classical grey prediction model-GM(1,1) in terms of accuracy.
Article
Engineering, Multidisciplinary
L. Li, S. X. Zhang, Y. Qiang, Z. Zheng, S. H. Li, C. S. Xia
Summary: This paper introduces an iteration-based combined prediction method for predicting landslide displacement, comparing its reliability with other methods and demonstrating its simplicity and promising prospects in engineering applications.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Construction & Building Technology
Li Li, Shi Xin Zhang, Shao Hong Li, Yue Qiang, Zhou Zheng, Dong Sheng Zhao
Summary: A new approach for risk assessment of debris flow is proposed in this paper, which proves to be effective based on data collected in Beichuan, Sichuan, China. The study also highlights the importance of considering the variations in results when using different weights for factors in sorting samples.
ADVANCES IN CIVIL ENGINEERING
(2021)
Article
Multidisciplinary Sciences
Li Li, Bo Ni, Yue Qiang, Shixin Zhang, Dongsheng Zhao, Ling Zhou
Summary: This paper proposes a new debris flow risk assessment method based on the Monte Carlo Simulation and an Improved Cloud Model. The method tests the consistency of coupling weights and determines the weight boundary of each evaluation index. The Monte Carlo Simulation is used to converge the weights, and the final weight value of each index is obtained using an Improved Cloud Model. The method is proved to be more reliable for debris flow prevention and control through comparison with other methods.
Article
Geochemistry & Geophysics
L. Z. Wu, S. H. Li, P. Sun, R. Q. Huang, B. Li
PURE AND APPLIED GEOPHYSICS
(2019)
