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Dynamic event-triggered consensus tracking control for nonlinear multi-agent systems with actuator failures and unknown dead zones 具有执行器失效和未知死区的非线性多智能体系统的动态事件触发一致性跟踪控制
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-28 DOI: 10.1016/j.asej.2025.103886
Ju Li , Junhong Chen , Fengjun Shang
In this paper, we investigate the problem of dynamic event-triggered consensus tracking control for nonlinear multi-agent systems (MASs) with actuator failures and unknown dead zones. The MASs involve mismatched unknown parameters, actuator failures, and unknown dead zones, which make the consensus control problem difficult. To this end, by using the bounded estimation method, smoothing function method, and adaptive technique, a distributed adaptive fault-tolerant control (FTC) scheme based on the backstepping technique is designed, which compensates adaptively for effects of actuator failures and unknown dead zones. Moreover, a new dynamic event-triggered control (DETC) strategy is developed to reduce the communication burden in contrast to the existing static event-triggered control. Based on the Lyapunov method, it is shown that the consensus tracking control can be achieved and the Zeno behavior does not occur. Finally, the effectiveness of the proposed control method is validated through two simulation examples.
本文研究了具有执行器失效和未知死区的非线性多智能体系统的动态事件触发一致性跟踪控制问题。由于存在未知参数不匹配、致动器失效和未知死区等问题,使得共识控制问题变得困难。为此,采用有界估计法、平滑函数法和自适应技术,设计了一种基于后退技术的分布式自适应容错控制方案,对执行器故障和未知死区影响进行自适应补偿。此外,与现有的静态事件触发控制相比,提出了一种新的动态事件触发控制(DETC)策略,以减少通信负担。基于Lyapunov方法,可以实现一致跟踪控制,且不发生Zeno行为。最后,通过两个仿真算例验证了所提控制方法的有效性。
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引用次数: 0
Enhancing smart manufacturing: a tensor-based ontology framework for predictive optimization using semantic digital twin 增强智能制造:基于张量的本体框架,用于使用语义数字孪生进行预测优化
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-27 DOI: 10.1016/j.asej.2025.103877
Sana Yasin , Umar Draz , Hazem M. El-Hageen , Tariq Ali , Yousef H. Alfaifi , Muhammad Ayaz , Low Tang Jung , El-Hadi M. Aggoune
The rapid advancement of Industry 4.0 has driven the need for intelligent, responsive manufacturing systems that can anticipate and mitigate disruptions, reduce downtime, and optimize performance. However, traditional manufacturing systems often rely on reactive maintenance strategies, leading to unexpected downtimes and increased operational costs. These limitations necessitate a shift toward predictive optimization for real-time condition monitoring and proactive failure prevention. This study presents a Tensor-Based Semantic Digital Twin (SDT) framework that integrates a hybrid CNN-LSTM model with ontology-based decision-making to provide a context-aware predictive optimization system. The SDT framework outperforms traditional methods, such as Deep Learning-Based Predictive Maintenance (DL-PdM) and Hybrid Anomaly Detection in Manufacturing (HAD-M), by significantly reducing equipment downtime and lowering costs per unit while maintaining high predictive accuracy and operational efficiency. The study demonstrates that SDTs provide real-time operational intelligence, ensuring manufacturing systems are more resilient, sustainable, and cost-effective. Unlike traditional approaches that rely on static models, the proposed framework enables adaptive learning from evolving sensor data, allowing manufacturing facilities to anticipate failures proactively and optimize resource utilization dynamically. By leveraging a hybrid CNN-LSTM model, the framework accurately predicts equipment failures, ensuring a 30% reduction in unexpected downtimes and a 20% improvement in energy consumption efficiency. Additionally, ontology-based decision-making enables context-aware automation, leading to an 18% decrease in maintenance costs and adaptive load balancing in dynamic industrial environments. Additionally, the proposed system extends beyond predictive maintenance by incorporating automated reactive control, making real-time adjustments to minimize inefficiencies. The findings establish a new standard for intelligent manufacturing, ensuring enhanced resilience, adaptability, and cost efficiency of smart manufacturing.
工业4.0的快速发展推动了对智能,响应式制造系统的需求,这些系统可以预测和减轻中断,减少停机时间并优化性能。然而,传统的制造系统通常依赖于被动维护策略,导致意外停机并增加运营成本。这些限制需要转向预测优化,以实现实时状态监测和主动故障预防。本研究提出了一个基于张量的语义数字孪生(SDT)框架,该框架将CNN-LSTM混合模型与基于本体的决策相结合,提供了一个上下文感知的预测优化系统。SDT框架优于传统方法,如基于深度学习的预测性维护(DL-PdM)和制造中的混合异常检测(hd - m),通过显着减少设备停机时间和降低单位成本,同时保持高预测精度和操作效率。该研究表明,sdt提供实时操作智能,确保制造系统更具弹性、可持续性和成本效益。与依赖静态模型的传统方法不同,所提出的框架能够从不断变化的传感器数据中进行自适应学习,使制造工厂能够主动预测故障并动态优化资源利用。通过利用CNN-LSTM混合模型,该框架可以准确预测设备故障,确保将意外停机时间减少30%,并将能耗效率提高20%。此外,基于本体的决策可以实现上下文感知自动化,从而在动态工业环境中降低18%的维护成本和自适应负载平衡。此外,拟议的系统通过集成自动反应控制来扩展预测性维护,进行实时调整以最大限度地减少效率低下。研究结果为智能制造建立了新的标准,确保了智能制造增强的弹性、适应性和成本效率。
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引用次数: 0
Dynamic behavior of an adjacent tunnel under blasting and collapse impact loads: a case study of high-rise building blasting demolition 爆破与崩塌冲击荷载作用下相邻巷道动力特性研究——以高层建筑爆破拆除为例
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-27 DOI: 10.1016/j.asej.2025.103892
Yuqing Xia, Yingkang Yao, Yongsheng Jia, Jinshan Sun, Nan Jiang
Blasting demolition is widely used for removing high-rise buildings due to its safety and efficiency, but induced vibrations and collapse impacts can damage nearby structures. To study the dynamic behavior of an adjacent subway tunnel subjected to blasting and collapse impact loads during high-rise building blasting demolition, a 24-story building demolition project is taken as a research case. Vibrometers and strain gauges are installed in the tunnel to record its dynamic response. Additionally, an elaborate 3D numerical model is established to simulate the collapse process and clarify three distinct impact load characteristics. It is indicated that blasting vibration from the explosion and the high-velocity collapse of the building’s upper parts have negligible effects on the tunnel. However, the impact load generated on the basement, resulting from the failure of the primary incision and the building’s subsequent subsidence, exerts a critical influence on the tunnel. A parameter analysis reveals the decisive effect of the Er/Es ratio. It indicates that segment stress, unlike PPV, is the more reliable criterion for evaluating segment safety under such impacts.
爆破拆除因其安全、高效而被广泛应用于高层建筑的拆除,但引起的振动和倒塌冲击会破坏附近的结构。为研究相邻地铁隧道在高层建筑爆破拆除过程中爆破和倒塌冲击荷载作用下的动力特性,以某24层建筑爆破拆除工程为研究案例。隧道内安装了测振仪和应变仪,记录隧道的动态响应。此外,还建立了一个精细的三维数值模型来模拟坍塌过程,并阐明了三种不同的冲击载荷特性。结果表明,爆炸产生的爆破振动和建筑物上部的高速倒塌对隧道的影响可以忽略不计。然而,由于主切口破坏和建筑物后续沉降对基底产生的冲击荷载对隧道产生至关重要的影响。参数分析揭示了Er/Es比的决定性作用。这表明,与PPV不同,在这种影响下,管段应力是评价管段安全性的更可靠的准则。
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引用次数: 0
An improved hybrid feature selection and classification framework for breast cancer detection using mammography images 一种改进的混合特征选择和分类框架,用于乳房x线摄影图像的乳腺癌检测
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-27 DOI: 10.1016/j.asej.2025.103897
Aniruddha Deka , Debashis Dev Misra , Munsifa Firdaus Khan Barbhuyan , Mudassir Khan , Mostaque Md. Morshedur Hassan , Mohammed Ashfaq Hussain
Breast cancer is one of the most common diseases that affects women around the world. Finding it early can help save lives. Doctors usually use tests like biopsy, ultrasound, CT scan, and mammography to detect breast cancer. In this study, we created a computer-based method that helps in detecting breast cancer more accurately. The process has four main steps — preprocessing, segmentation, feature selection, and classification. First, we clean the mammogram images using a filter to remove unwanted noise. Next, we separate the important part of the image using a special method called Thresholding-Based Level Set. Then, we choose only the most important details (features) from the image using a new hybrid method called Improved Grey Wolf Optimization with Seagull Optimization Algorithm. Finally, we use a machine learning model named CatBoost to identify if the tumor is benign (non-cancerous) or malignant (cancerous). When tested on a dataset, our method showed excellent results with 99.2 % accuracy. This shows that our model can help doctors detect breast cancer early and more correctly.
乳腺癌是影响世界各地妇女的最常见疾病之一。及早发现有助于挽救生命。医生通常使用活检、超声波、CT扫描和乳房x光检查来检测乳腺癌。在这项研究中,我们创造了一种基于计算机的方法,有助于更准确地检测乳腺癌。该过程有四个主要步骤-预处理,分割,特征选择和分类。首先,我们使用过滤器来清除乳房x光图像,去除不必要的噪声。接下来,我们使用一种称为基于阈值的水平集的特殊方法分离图像的重要部分。然后,我们使用一种新的混合方法,即改进灰狼优化和海鸥优化算法,从图像中选择最重要的细节(特征)。最后,我们使用一个名为CatBoost的机器学习模型来识别肿瘤是良性(非癌性)还是恶性(癌性)。在数据集上进行测试时,我们的方法显示出99.2%的准确率。这表明我们的模型可以帮助医生更早、更准确地发现乳腺癌。
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引用次数: 0
Adaptive PolyKAN-based autoencoder for fault detection and classification in wind and solar power systems 基于自适应polykan自编码器的风电和太阳能系统故障检测与分类
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-26 DOI: 10.1016/j.asej.2025.103884
Khadija Attouri , Majdi Mansouri , Abdelmalek Kouadri
This paper presents an advanced fault diagnosis framework for renewable energy systems by leveraging a novel Adaptive Polynomial Kolmogorov Arnold Network (Adaptive PolyKAN). The proposed method is evaluated on two distinct applications: a wind energy conversion system and a grid-connected photovoltaic (PV) system, each characterized by complex, nonlinear fault patterns. A comprehensive comparison is conducted against a range of classical and neural classifiers, including Random Forest (RF), Support Vector Machine (SVM), and others. Experimental results demonstrate that Adaptive PolyKAN consistently achieves superior classification accuracy, reaching 99.96 % for wind data and 95.61 % for PV data, outperforming conventional methods across all performance metrics. To improve computational efficiency, an autoencoder-based dimensionality reduction strategy is incorporated, resulting in a reduction of execution time by over 88 % and memory usage by 40 %, while preserving high diagnostic accuracy, maintaining 99.96 % on the wind data and increasing to 96.47 % on the PV data. The results confirm the robustness, adaptability, and efficiency of the proposed framework, highlighting its potential for intelligent fault diagnosis in complex renewable energy systems.
本文利用一种新的自适应多项式Kolmogorov Arnold网络(Adaptive PolyKAN),提出了一种先进的可再生能源系统故障诊断框架。该方法在两个不同的应用中进行了评估:风能转换系统和并网光伏(PV)系统,每个系统都具有复杂的非线性故障模式。对一系列经典分类器和神经分类器进行了全面的比较,包括随机森林(RF),支持向量机(SVM)等。实验结果表明,Adaptive PolyKAN在风能数据和光伏数据上的分类准确率分别达到99.96%和95.61%,在所有性能指标上都优于传统方法。为了提高计算效率,采用了基于自动编码器的降维策略,使执行时间减少了88%以上,内存使用减少了40%,同时保持了较高的诊断准确性,在风数据上保持了99.96%,在PV数据上提高到96.47%。结果证实了该框架的鲁棒性、适应性和有效性,突出了其在复杂可再生能源系统智能故障诊断方面的潜力。
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引用次数: 0
A novel deep learning-based control for voltage sag prediction and DVR–LVRT coordination in grid-connected wind turbine systems 基于深度学习的并网风电系统电压暂降预测与DVR-LVRT协调控制
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-23 DOI: 10.1016/j.asej.2025.103882
Mohamed A. Ahmed, Mona A. Bayoumi
This study proposes a novel deep feedforward neural network (DFNN)-based control for voltage sag prediction and dynamic voltage restorer (DVR) integration with low-voltage ride-through (LVRT) to improve voltage stability and energy efficiency in wind turbine systems. Proposed approach precisely predicts sag duration, adaptively regulates DVR activation according to LVRT profile to avoid redundant compensation. This predictive control reduces DVR operating time and energy consumption while maintaining voltage stability. Synthetic datasets representing various grid conditions, including distorted voltage, enable DFNN to achieve a prediction accuracy near 99 %, a time error margin of 0.005–0.02 s and a response time of 0.016 s. This precise prediction improves DVR energy efficiency by nearly 30 % per long-duration fault. Compared to a support vector regression (SVR) model, DFFN achieves 33.3 % faster response and lower error metrics. Simulation results validated in a MATLAB/Simulink demonstrate effectiveness of proposed approach in enhancing LVRT capability and overall grid efficiency.
本文提出了一种新的基于深度前馈神经网络(DFNN)的电压暂降预测和动态电压恢复器(DVR)与低压穿越(LVRT)集成的控制方法,以提高风力发电系统的电压稳定性和能效。该方法精确预测暂降持续时间,根据LVRT剖面自适应调节DVR激活,避免冗余补偿。这种预测控制减少了DVR运行时间和能耗,同时保持电压稳定。代表各种网格条件(包括扭曲电压)的合成数据集使DFNN能够实现接近99%的预测精度,时间误差范围为0.005-0.02 s,响应时间为0.016 s。这种精确的预测使每次长时间故障的DVR能效提高了近30%。与支持向量回归(SVR)模型相比,DFFN的响应速度快了33.3%,误差指标更低。MATLAB/Simulink仿真结果验证了该方法在提高LVRT性能和整体网格效率方面的有效性。
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引用次数: 0
A hybrid data envelopment analysis and artificial intelligence framework for sustainable supplier selection: a case study in the petrochemical industry 可持续供应商选择的混合数据包络分析和人工智能框架:石化行业的案例研究
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-21 DOI: 10.1016/j.asej.2025.103871
Maedeh GholamAzad, Alireza Eydi
As global industrial operations expand, the complexity and volume of suppliers have increased, making sustainable supplier selection (SSS) a strategic imperative for resilient supply chains (SCs). Traditional evaluation methods often fail to handle large datasets and dynamic sustainability metrics, resulting in suboptimal decisions. This study introduces a novel hybrid intelligent framework that integrates Most Productive Scale Size Data Envelopment Analysis (MPSS-DEA) with three Artificial intelligence (AI) algorithms—Artificial Neural Networks (ANNs), K-Nearest Neighbors (KNN), and Chi-squared Automatic Interaction Detection (CHAID)—to enhance both accuracy and scalability in supplier evaluation. Applied to 362 suppliers and 38 sustainability criteria in the petrochemical industry, the proposed framework achieved high classification accuracies of 92.5% (DEA-CHAID), 91.9% (DEANN), and 91.4% (DEA-KNN). The model also demonstrated strong discrimination power, with ROC AUC scores of 0.96, 0.95, and 0.94, respectively. Predictor importance analysis revealed that some of the features, such as R2, SE2, QA4, CA6, and DE3, were the most influential features across all models. Beyond performance metrics, the framework offers real-time supplier replacement, reduced computational complexity, and modular adaptability across industries. It supports ethical and sustainable sourcing by integrating economic, environmental, and social dimensions into decision-making. The intelligent architecture enables lifecycle analysis, promotes transparency, and aligns with global sustainability standards. This research contributes a scalable, interpretable, and data-driven solution for sustainable supplier selection, bridging the gap between traditional DEA models and modern artificial intelligence (AI) techniques. Its applicability across diverse industrial contexts positions it as a robust tool for strategic procurement and supply chain resilience.
随着全球工业运营的扩大,供应商的复杂性和数量都在增加,使得可持续供应商选择(SSS)成为弹性供应链(sc)的战略当务之急。传统的评估方法往往不能处理大数据集和动态可持续性指标,导致次优决策。本研究引入了一种新的混合智能框架,该框架将最生产规模数据包络分析(MPSS-DEA)与三种人工智能(AI)算法——人工神经网络(ann)、k近邻(KNN)和卡方自动交互检测(CHAID)——集成在一起,以提高供应商评估的准确性和可扩展性。应用于石化行业的362家供应商和38个可持续性标准,该框架的分类准确率达到了92.5% (DEA-CHAID)、91.9% (DEANN)和91.4% (DEA-KNN)。模型的ROC AUC得分分别为0.96、0.95和0.94,具有较强的辨别力。预测因子重要性分析显示,一些特征,如R2、SE2、QA4、CA6和DE3,是所有模型中最具影响力的特征。除了性能指标,该框架还提供实时供应商替换、降低计算复杂性和跨行业模块化适应性。它通过将经济、环境和社会维度纳入决策,支持道德和可持续的采购。智能架构支持生命周期分析,提高透明度,并与全球可持续性标准保持一致。该研究为可持续供应商选择提供了可扩展、可解释和数据驱动的解决方案,弥合了传统DEA模型与现代人工智能(AI)技术之间的差距。它在不同行业背景下的适用性使其成为战略采购和供应链弹性的强大工具。
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引用次数: 0
Solving time fractional diffusion-wave equation using hyperbolic polynomial B-splines: A uniform grid approach 用双曲多项式b样条解时间分数阶扩散波方程:一种均匀网格方法
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-21 DOI: 10.1016/j.asej.2025.103868
Aleeza Kiran , Muhammad Yaseen , Aziz Khan , Thabet Abdeljawad , Manar A. Alqudah , Rajermani Thinakaran
In this study, we present an efficient numerical scheme based on uniform hyperbolic polynomial B-splines for solving the time-fractional diffusion-wave equation involving the Caputo derivative. This equation models various physical phenomena including anomalous diffusion and complex dynamical behavior. The proposed method ensures a smooth and continuous approximation that effectively captures both local and global features of the solution such as sharp gradients and long-range memory effects. The key advantage of uniform hyperbolic polynomial B-splines lies in their flexibility and high accuracy across the computational domain. Stability and convergence analyses are carried out to confirm the method’s robustness and error control. Finally, numerical results are compared with those reported in existing literature to demonstrate the accuracy and reliability of the scheme as process innovation.
在本研究中,我们提出了一个基于一致双曲多项式b样条的有效数值格式,用于求解包含Caputo导数的时间分数阶扩散波方程。该方程模拟了各种物理现象,包括异常扩散和复杂的动力学行为。该方法保证了平滑和连续的逼近,有效地捕获了解的局部和全局特征,如尖锐梯度和长期记忆效应。一致双曲多项式b样条的主要优点在于其跨计算域的灵活性和高精度。通过稳定性和收敛性分析,验证了该方法的鲁棒性和误差控制能力。最后,将数值结果与已有文献报道的结果进行了比较,验证了该方案作为工艺创新方案的准确性和可靠性。
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引用次数: 0
Enhanced IoT security: privacy-preserving federated learning model for accurate, real-time intrusion detection across devices 增强物联网安全性:保护隐私的联邦学习模型,用于跨设备的准确、实时入侵检测
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-21 DOI: 10.1016/j.asej.2025.103866
A. Puviarasu , Sudha V K
Federated learning (FL) has been proposed as an effective solution in the context of intrusion detection in IoT networks, where models can be trained collaboratively with the security of raw data protection. In this paper we present a privacy-preserving FL framework based on light weight neural network, differential privacy (DP) and homomorphic encryption (HE). With a dataset of 1,191,264 instances and 47 attributes, the proposed model conducted on the IoT Intrusion Detection Dataset available on Kaggle produces overall accuracy (93.5), precision (94.2), recall (93.4), and the F1-score (94.2), with the detection time of 90–130 ms and no distinction between the attacks, where detection latency was considered in this study. At the attack level the model delivered 94.1 %, 92.5 %, and 93.6 % accuracies on DoS, DDoS, and Mirai respectively, and above 85 % accuracy on Malware and Web-based attacks. DP experiments showed that augmenting the privacy budget parameter 0.5 to 20.0 increased the levels of accuracy by 2.6 % to 94.0 %, and decreased the computational time 150 ms to 121 ms, depicting a compromise between privacy and performance. HE experiments likewise exhibited a negligible accuracy reduction (94.1 % to 93.5 %) between no encryption to complete homomorphic encryption, but required more computation time (120 ms to 200 ms). Devices-level testing demonstrated that the model had > 91 % accuracy at the low-end (0.5 GHz CPU, 128 MB memory) and up to 94.5 % accuracy with 110 ms inference time on powerful processors, irrespective of whether or not the sensor was heterogeneous, demonstrating a viable solution to the heterogeneous IT situation. Audit mechanisms further enhanced greater compliance of 0 % to 99 % with minimal reduction in accuracy (< 0.8 %). The results show that privacy-preserving intrusion detection specifically can be performed with real-time intrusion detection, high detection gene, and privacy guarantees in resource-constrained IoT networks.
联邦学习(FL)已被提出作为物联网网络入侵检测背景下的有效解决方案,其中模型可以与原始数据保护的安全性协同训练。本文提出了一种基于轻量级神经网络、差分隐私(DP)和同态加密(HE)的隐私保护FL框架。在Kaggle上可用的物联网入侵检测数据集上进行的数据集有1,191,264个实例和47个属性,所提出的模型产生了总体准确性(93.5),精度(94.2),召回率(93.4)和f1分数(94.2),检测时间为90-130毫秒,攻击之间没有区别,本研究中考虑了检测延迟。在攻击层面,该模型对DoS、DDoS和Mirai的准确率分别为94.1%、92.5%和93.6%,对恶意软件和基于web的攻击的准确率超过85%。DP实验表明,将隐私预算参数增加0.5到20.0,准确率水平提高2.6%到94.0%,计算时间减少150 ms到121 ms,在隐私和性能之间取得了折衷。HE实验同样显示,在没有加密到完全同态加密之间,精度降低可以忽略不计(94.1%到93.5%),但需要更多的计算时间(120 ms到200 ms)。设备级测试表明,无论传感器是否异构,该模型在低端(0.5 GHz CPU, 128 MB内存)下具有>; 91%的准确率,在强大的处理器上具有高达94.5%的准确率和110 ms的推理时间,这证明了针对异构IT情况的可行解决方案。审计机制进一步提高了0%到99%的合规性,而准确性的降低最小(0.8%)。结果表明,在资源受限的物联网网络中,具有实时入侵检测、高检测基因和隐私保障的保护隐私入侵检测是有效的。
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引用次数: 0
Extended fractional hermite-hadamard type integral inequalities for h-convex functions with 2D and 3D graphical illustrations h-凸函数的扩展分数hermite-hadamard型积分不等式,附2D和3D图解
IF 5.9 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-11-20 DOI: 10.1016/j.asej.2025.103819
Akhtar Abbas , Fazila Fiyaz , Shahid Mubeen , Mdi Begum Jeelani , Ghaliah Alhamzi
In this paper, we establish new fractional Hermite–Hadamard type inequalities using k-Riemann–Liouville fractional integrals for differentiable h-convex functions. By employing k-Riemann Riouville fractional integrals and differentiable h-convex functions, our results extend and refine the existing inequalities in literature and show the connection between them. We discuss special cases of our derived inequalities which highlight the applicability and novelty of our approach. Furthermore, to support and visualize the theoretical findings, we provide detailed 2D and 3D graphical verifications of the main inequalities. These illustrations offer deeper insights into the behavior of the inequalities and demonstrate their practical relevance. Applications and future research directions are also addressed.
本文利用可微h-凸函数的k-Riemann-Liouville分数阶积分建立了新的分数阶Hermite-Hadamard型不等式。通过使用k-Riemann Riouville分数积分和可微h-凸函数,我们的结果扩展和完善了文献中现有的不等式,并展示了它们之间的联系。我们讨论了我们的推导不等式的特殊情况,突出了我们的方法的适用性和新颖性。此外,为了支持和可视化理论发现,我们提供了主要不平等的详细二维和三维图形验证。这些插图提供了对不平等行为的更深入的见解,并展示了它们的实际相关性。展望了应用前景和未来的研究方向。
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引用次数: 0
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