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Engineering, Electrical & Electronic
Kai Liu et al.
Summary: This paper proposes a novel thermal defect detection method, which investigates derivative curves characteristics and deduces mathematical expressions for quantitatively detecting defects. Experimental results demonstrate that the proposed method can effectively and accurately detect thermal defects, and its feasibility is validated in the practical application on vehicle cables.
Article
Automation & Control Systems
Zhonghao Xie et al.
Summary: This paper proposes a robust method for PLS based on the idea of least trimmed squares (LTS), which effectively deals with high-dimensional regressors. By formulating the LTS problem as a concave maximization problem, the complexity of solving LTS is simplified. The results from simulation and real data sets demonstrate the effectiveness and robustness of the proposed approach.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2022)
Article
Mathematics, Applied
Mounirah Areshi et al.
Summary: In this paper, two different methods are used to find the solution of the time-fractional Newell-Whitehead-Segel equation, which plays an efficient role in describing stripe patterns in nonlinear systems. The proposed methods provide numerical results that are in strong agreement with an exact solution, and the effectiveness of these methods is demonstrated through graphs and tables. Furthermore, the results show that the solution approaches the exact solution as the fractional order tends towards an integer order. The proposed methods are interesting, easy to use, and highly accurate for solving various nonlinear fractional-order partial differential equations.
Article
Mathematics
Mohammed Kbiri Alaoui et al.
Summary: In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find the solution to nonlinear fractional Gardner and Cahn-Hilliard equations. The proposed methods were compared with exact solutions and other methods, showing accuracy and validity.
Article
Mathematics, Interdisciplinary Applications
A. A. Alderremy et al.
Summary: In this article, we solve nonlinear systems and coupled Burgers equations using two different methods and employing Laplace transform and Atangana-Baleanu fractional derivative operator. The convergence of the method is successfully demonstrated and mathematically proved by comparing the obtained results with exact solutions through graphs and tables. Moreover, the results obtained at different fractional orders are compared, confirming the suitability and effectiveness of the proposed techniques in solving partial differential equations or systems.
Article
Engineering, Multidisciplinary
Humaira Yasmin et al.
Summary: This article discusses the fractional-order analysis of one- and two-dimensional nonlinear systems and compares the results obtained using the proposed methods with the exact solution. The effectiveness of the methods is demonstrated through graphs and tables, confirming their suitability for solving partial differential equations or systems of partial differential equations.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Humaira Yasmin et al.
Summary: This paper applies modified analytical methods to analyze one and two-dimensional nonlinear systems of coupled Burgers and Hirota-Satsuma KdV equations. The proposed problems are solved using the Atangana-Baleanu fractional derivative operator and the Elzaki transform. The results are compared to the exact solution, and the convergence of the technique is mathematically proven. The suggested techniques are shown to be effective, simple, and accurate for solving partial differential equations or systems of partial differential equations.
Article
Materials Science, Multidisciplinary
Kang-Jia Wang
Summary: The optical solitons of the generalized third-order nonlinear Schrodinger's equation were investigated using a new one-step method called the direct mapping method. Four sets of soliton solutions were constructed in one step, proving the simplicity and effectiveness of the proposed method. This study is expected to inspire new approaches to the study of partial differential equations in physics.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Ahmed M. Zidan et al.
Summary: This article demonstrates the solution to the time-fractional Fisher's equation using two well-known analytical methods. The proposed techniques, a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform, show high accuracy and reliability through illustrative examples. The benefits of these techniques include a small number of calculations and applicability in various fields of applied sciences.
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Mathematics, Applied
M. Mossa Al-Sawalha et al.
Summary: The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries -modified Korteweg-de Vries system is obtained using a natural decomposition method in conjunction with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The results demonstrate that the natural decomposition technique is a very user-friendly and reliable method for dealing with fractional order nonlinear problems.
Article
Mathematics, Applied
Thongchai Botmart et al.
Summary: In this paper, the Natural decomposition approach and nonsingular kernel derivatives were used to explore the modified Boussinesq and approximate long wave equations. Convergence analysis, error analysis, and verification of the approach were performed. The results show that the suggested scheme is computationally accurate and effective in solving fractional coupled nonlinear complicated phenomena.
Article
Mathematics, Interdisciplinary Applications
A. A. Alderremy et al.
Summary: This article successfully solves nonlinear systems of equations using two different methods, comparing the results with exact solutions to confirm effectiveness and accuracy. Additionally, the use of fractional orders allows the results to approximate the exact solution, demonstrating the flexibility of the methods.
Article
Computer Science, Artificial Intelligence
Hajar Farhan Ismael et al.
Summary: In this work, novel solutions of nematicons within liquid crystals with three types of nonlinearity were constructed using the generalized exponential rational function method. The diversity between solutions obtained via this method and other methods was observed. Various types of solitons and complex solutions were successfully constructed, helping to better understand the characteristics of nematicons in liquid crystals.
Article
Engineering, Biomedical
Yushan Tang et al.
Summary: The study combined the finite element method with mass-spring model to estimate parameters and determine the soft tissue model using real measurement data. The improved model can better consider timeliness and accuracy, and accurately simulate soft tissue, showing higher data fitting and smaller force values under the same displacement.
BIOMEDICAL SIGNAL PROCESSING AND CONTROL
(2021)
Article
Computer Science, Artificial Intelligence
Wenfeng Zheng et al.
Summary: This paper constructs a knowledge base graph embedding module to extend the versatility of knowledge-based VQA models. By extracting core entities from images and text and performing sub-graph embedding, the accuracy of knowledge-based VQA models is improved.
PATTERN RECOGNITION
(2021)
Article
Chemistry, Multidisciplinary
Wenfeng Zheng et al.
Summary: This paper proposes a multi-layer semantic representation network for sentence representation, which enhances the accuracy and comprehensiveness of sentence representation through multi-attention mechanism and relative position mask.
APPLIED SCIENCES-BASEL
(2021)
Article
Multidisciplinary Sciences
Pongsakorn Sunthrayuth et al.
Summary: This article introduces two well-known computational techniques for solving the time-fractional Fornberg-Whitham equations and presents a graphical representation to show the reliability and accuracy of the suggested approaches.Comparative solution analysis via graphs also demonstrates the higher reliability and accuracy of the current techniques.
Article
Engineering, Multidisciplinary
Mehmet Yavuz et al.
Summary: Fractional order differential equations are widely used in modeling complex physical and natural phenomena. This manuscript examines the fractional order Schrodinger-KdV equation and establishes the exact solution using the fixed-point theorem and modified Laplace decomposition method. Numerical simulations and comparison between analytical and numerical approximations are also presented in the study.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Kamsing Nonlaopon et al.
Summary: This paper implements the Laplace homotopy perturbation transform technique to study the fractional-order Whitham-Broer-Kaup equations. The efficiency of both operators is confirmed, and a comparison is made between solutions obtained from two fractional-order derivatives.
Article
Mathematics
Vladislav N. Kovalnogov et al.
Summary: The purpose of this study is to construct a new Runge-Kutta pair that outperforms existing methods in dealing with problems with periodic solutions. By tuning parameters, the new method shows superior performance on a pair of oscillators compared to other well-known methods.
Article
Computer Science, Information Systems
Wenfeng Zheng et al.
Summary: In visual reasoning, deep learning has greatly improved the accuracy of results. By introducing semantic representation, a higher-level representation, more accurate results can be obtained. This study lays the foundation for introducing different levels of knowledge representation into deep learning in the future.
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Mathematics, Applied
Mehmet Yavuz et al.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2020)
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Chemistry, Multidisciplinary
Ji-Huan He et al.
JOURNAL OF MATHEMATICAL CHEMISTRY
(2020)
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Computer Science, Information Systems
Run Ye et al.
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Physics, Multidisciplinary
Mehmet Yavuz et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2018)
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Physics, Multidisciplinary
Mostafa Eslami et al.
European Physical Journal Plus
(2013)
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Chandradeepa D. Dhaigude et al.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2012)
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Houria Triki et al.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2011)
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Li-Hua Zhang et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2010)
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Semih Kucukarslan
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2009)
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D. D. Ganji et al.
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A Biswas
OPTICAL FIBER TECHNOLOGY
(2003)
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A Trombettoni et al.
PHYSICAL REVIEW LETTERS
(2001)
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JC Bronski et al.
PHYSICAL REVIEW LETTERS
(2001)
