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-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH MAXIMA ON TIME SCALES

Journal of Mathematical Sciences 2024年第1期289卷 1-13页

作者： Taqbibt, Abdellah Chefnaj, Najat Hilal, Khalid Melliani, Said Applied Mathematics and Scientific Computing Laboratory Sultan Moulay Slimane University Beni Mellal Morocco

In this paper, we demonstrate the existence and uniqueness of solutions for a class of initial value problems in differential equations with maxima, involving the $$\psi$$ -Caputo fractional order on time scales. Our main theorem is established through the application of the contraction principle of Banach, employing a combination of Picard and weak Picard operator techniques to obtain data dependence results on the parameters. Furthermore, an illustrative example is provided to demonstrate the practical utility of our theoretical findings.

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Nehari manifold and fibering map approach for fractional p(.)-Laplacian Schrödinger system

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SeMA Journal 2024年第4期81卷 729-751页

作者： El-Houari, Hamza Chadli, Lalla Saadia Hicham, Moussa Faculty of Sciences and Techniques Béni Mellal Research Laboratory “Applied Mathematics and Scientific Computing” University Sultan Moulay Slimane Campus Mghilla BP 523 Béni Mellal 23000 Morocco

In this paper we extended the results of Biswas & Tiwari named Nehari manifold approach for fractional p(· ) -Laplacian system involving concave-convex nonlinearities (2020). We study the existence and multiplicity of solutions to the fractional Schrödinger problem system with Dirichlet boundary condition by using the Nehari manifold approach. The nonlinearities is not satisfied Ambrosetti–Rabinowitz condition, monotonocity or convexity conditions, and can be discontinuous in nature. © 2023, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.

关键词： 35J20 35J60 35S15 46E35 58E30 Fibering map approach Fractional p(.)-Laplacian operator Nehari manifold Schrödinger problems

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A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

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Communications on applied mathematics and Computation 2023年第1期5卷 403-427页

作者： Liang Li Jun Zhu Chi-Wang Shu Yong-Tao Zhang Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Applied and Computational Mathematics and Statistics University of Notre DameNotre DameIN 46556USA

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local ***,they are easy to be applied to a general hyperbolic *** deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the *** this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing *** experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the *** results show highorder accuracy and good performance of the ***,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state *** examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

关键词： Fixed-point fast sweeping methods Multi-resolution WENO schemes Steady state ILW procedure Convergence

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RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

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Communications on applied mathematics and Computation 2024年第3期6卷 1575-1599页

作者： Jun Zhu Chi-Wang Shu Jianxian Qiu State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005FujianChina

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

关键词： RKDG method Steady-state problem Multi-resolution WENO limiter Triangular mesh Machine zero

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Existence results for anti-periodic fractional coupled systems with p- Laplacian operator via measure of noncompactness in Banach spaces

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Journal of Mathematical Sciences (United States) 2023年第2期271卷 162-175页

作者： El Mfadel, Ali Melliani, Said Elomari, M’hamed Superior School of Technology Sultan Moulay Slimane University Khenifra Morocco Laboratory of Applied Mathematics and Scientific Computing Sultan Moulay Slimane University Beni Mellal Morocco

The aim of this paper is to investigate the existence of anti-periodic solutions for a nonlinear coupled system of Ψ - Caputo fractional differential equations with p- Laplacian operator in a Banach space. The proofs of our main results are based on Mönch’s fixed point theorem and some basic tools of Ψ - Caputo fractional calculus paired with measures of noncompactness. As an application, our theoretical results have been illustrated by providing an interesting example. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Measures of noncompactness p- Laplacian operator Ψ -Caputo fractional derivative Ψ -fractional integral

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Bayesian inference of the basic reproduction number for a SIR epidemic model

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Biostatistics and Epidemiology 2022年第1期6卷 128-143页

作者： Qaffou, Abdelaziz El Maroufy, Hamid Zbair, Mokhtar Laboratory of Applied Mathematics and Scientific Computing Department of Applied Mathematics Faculty of Sciences and Techniques Sultan Moulay Slimane University–Beni-Mellal Beni-Mellal Morocco Laboratory of Mathematics and Application Department of Applied Mathematics Faculty of Sciences and Techniques Sultan Moulay Slimane University–Beni-Mellal Beni-Mellal Morocco

This paper is concerned with the Bayesian estimation for the basic reproduction number (Formula presented.), defined as the expected number of new infectious from one infected individual in a fully susceptible population through the entire duration of the infectious period. This parameter is of great importance within epidemic modeling because no epidemic can occur if (Formula presented.) and an epidemic occurs if (Formula presented.). Estimation of (Formula presented.), or equivalent parameters in more complex models, can usually be achieved via Markov chain Monte Carlo (MCMC) methods. We will adopt the Bayesian method proposed by Eraker [MCMC analysis of diffusion models with application to finance. J Bus Econ Statist. 2001;19(2):177–191] in the context of financial models. The method consists of augmenting the low-frequency observations by the insertion of a finite number of latent data between two consecutive observations. We develop MCMC methods for inference to explore a posterior distribution of (Formula presented.) and of missing data. We illustrate the performance of the estimators on both synthetic data and real epidemic from the SIR (Susceptible-Infective-Removed) epidemic model and compare the results with the maximum likelihood (ML) method. © 2022 International Biometric Society–Chinese Region.

关键词： Basic reproduction number Bayesian inference Maximum likelihood method MCMC method SIR epidemic model

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What Does ChatGPT Say:The DAO from Algorithmic Intelligence to Linguistic Intelligence

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IEEE/CAA Journal of Automatica Sinica 2023年第3期10卷 575-579页

作者： Fei-Yue Wang Qinghai Miao Xuan Li Xingxia Wang Yilun Lin School of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049China State Key Laboratory for Management and Control of Complex Systems Chinese Academy of SciencesBeijing 100190China Virtual Reality Fundamental Research Laboratory Department of Mathematics and TheoriesPeng Cheng LaboratoryShenzhen 518000China Urban Computing Lab Department of Applied ResearchShanghai AI LaboratoryShanghai 200232China IEEE

THE well-known ancient Chinese philosopher Lao Tzu(老子)or Laozi(6th~4th century BC during the Spring and Autumn period)started his classic Tao Teh Ching《道德经》or Dao De Jing(see Fig.1)with six Chinese characters:"道(Dao)可(Ke)道(Dao)非(Fei)常(Chang)道(Dao)",which has been traditionally interpreted as“道可道,非常道”or"The Dao that can be spoken is not the eternal Dao".

关键词： DAO Intelligence Spring

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in Computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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Modified fuzzy clustering algorithm based on non-negative matrix factorization locally constrained

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Journal of Ambient Intelligence and Humanized computing 2023年第8期14卷 11373-11383页

作者： Li, Xiangli Fan, Xuezhen Lu, Xiyan School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin541004 China Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin541004 China Guangxi Applied Mathematics Center Guilin University of Electronic Technology Guilin541004 China

The fuzzy C-means (FCM) algorithm is a classical clustering algorithm which is widely used. However, especially for high-dimensional data sets with complex structures, the large-scale calculation of FCM suffers from decreasing clustering effect. In order to improve the clustering performance, we propose two new modified fuzzy clustering algorithms—modified fuzzy clustering algorithm based on non-negative matrix factorization (MFCM-NMF) and modified fuzzy clustering algorithm based on non-negative matrix factorization with local constraint (MFCM-LCNMF). Since MFCM-NMF combines NMF with modified FCM, the algorithm can use the dimensionality reduction technology of NMF, which greatly improves the computational efficiency. MFCM-LCNMF introduces NMF with local linear constraints into modified FCM, and it has a new objective function and adopts a new algorithm for alternate iteration. In the iterative process, the new membership update formula is utilized for the samples selected by the triangle inequality, which not only reduces the amount of calculation, but also obtains a higher clustering quality. Finally, a number of experiments on many data sets verify that MFCM-NMF and MFCM-LCNMF are more effective compared with other state-of-the-art methods. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Non-negative matrix factorization

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Critical factors inhibiting information and communication technology (ICT) adoption in Côte d'Ivoire: a study of small and medium enterprises (SMEs) in metropolitan Abidjan

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International Journal of Technology, Policy and Management 2024年第1期24卷 19-49页

作者： Assiélou, N'Doli Guillaume Bourgault, Mario Department of Fundamental and Applied Sciences Mathematics and Computing Laboratory Nangui Abrogoua University Côte d'Ivoire 02 Abidjan 02 AbidjanBP 801 Ivory Coast Department of Mathematics and Industrial Engineering Polytechnique Montreal P.O. Box 6079 Station Centre-ville MontréalQCH3C 3A7 Canada

The paper aims to investigate and categorise the barriers influencing information and communication technology (ICT) adoption among small and medium-sized enterprises (SMEs). A questionnaire-based survey was used to collect data from 77 owners/managers of SMEs in metropolitan Abidjan, Côte d'Ivoire. A research framework based on the technology-organisationenvironment- individual-economy (T-O-E-I-E) model was used to guide the research effort. The results suggest that technological, economic and environmental factors such as unreliable basic fixed internet, cybercrime, a lack of government support and a high cost of access to fixed broadband internet are the most significant barriers to ICT adoption in the sample. Manufacturing firms had the most difficulties adopting ICTs;smaller enterprises also had more difficulties. The findings of this study offer valuable insights to SME owners/managers, policy-makers, financial institutions and local ICT companies wishing to understand why SMEs are slow to adopt ICTs, and actions that can be taken to strengthen the level of ICT adoption among SMEs. © 2024 Inderscience Enterprises Ltd.

关键词： ICT adoption small and medium-sized enterprises T-O-E-I-E barriers critical factors Côte d'Ivoire

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