Fractal and Fractional最新文献_第10页

Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity 考虑传热和粘度的液气混合气泡中分数阶Kudryashov-Sinelshchikov方程的传播孤子解的探索

2区数学

Fractal and Fractional Pub Date : 2023-10-24 DOI: 10.3390/fractalfract7110773

Rashid Ali, Ahmed S. Hendy, Mohamed R. Ali, Ahmed M. Hassan, Fuad A. Awwad, Emad A. A. Ismail

{"title":"Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity","authors":"Rashid Ali, Ahmed S. Hendy, Mohamed R. Ali, Ahmed M. Hassan, Fuad A. Awwad, Emad A. A. Ismail","doi":"10.3390/fractalfract7110773","DOIUrl":"https://doi.org/10.3390/fractalfract7110773","url":null,"abstract":"In this research work, we investigate the complex structure of soliton in the Fractional Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study involves the development of soliton solutions using the modified Extended Direct Algebraic Method (mEDAM). This approach involves a key variable transformation, which successfully transforms the model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series form solution, the NODE is turned into a system of algebraic equations, allowing us to construct soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures. The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional, three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects such as optical fibre research, plasma physics, and a variety of applied sciences.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"8 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional Simpson-like Inequalities with Parameter for Differential s-tgs-Convex Functions 微分s-tgs-凸函数的带参数的分数阶类simpson不等式

2区数学

Fractal and Fractional Pub Date : 2023-10-24 DOI: 10.3390/fractalfract7110772

Meriem Merad, Badreddine Meftah, Hamid Boulares, Abdelkader Moumen, Mohamed Bouye

引用次数: 0

Positive Solutions for Some Semipositone Fractional Boundary Value Problems on the Half-Line 半线上若干半正数分数边值问题的正解

2区数学

Fractal and Fractional Pub Date : 2023-10-24 DOI: 10.3390/fractalfract7110774

Imed Bachar

引用次数: 0

Oxidopamine-Induced Nuclear Alterations Quantified Using Advanced Fractal Analysis: Random Forest Machine Learning Approach 使用高级分形分析量化氧化多巴胺诱导的核改变:随机森林机器学习方法

2区数学

Fractal and Fractional Pub Date : 2023-10-23 DOI: 10.3390/fractalfract7100771

Igor Pantic, Nikola Topalovic, Peter R. Corridon, Jovana Paunovic

{"title":"Oxidopamine-Induced Nuclear Alterations Quantified Using Advanced Fractal Analysis: Random Forest Machine Learning Approach","authors":"Igor Pantic, Nikola Topalovic, Peter R. Corridon, Jovana Paunovic","doi":"10.3390/fractalfract7100771","DOIUrl":"https://doi.org/10.3390/fractalfract7100771","url":null,"abstract":"Fractal analysis (FA) is a contemporary computational technique that can assist in identifying and assessing nuanced structural alterations in cells and tissues after exposure to certain toxic chemical agents. Its application in toxicology may be particularly valuable for quantifying structural changes in cell nuclei during conventional microscopy assessments. In recent years, the fractal dimension and lacunarity of cell nuclei, considered among the most significant FA features, have been suggested as potentially important indicators of cell damage and death. In this study, we demonstrate the feasibility of developing a random forest machine learning model that employs fractal indicators as input data to identify yeast cells treated with oxidopamine (6-hydroxydopamine, 6-OHDA), a powerful toxin commonly applied in neuroscience research. The model achieves notable classification accuracy and discriminatory power, with an area under the receiver operating characteristics curve of more than 0.8. Moreover, it surpasses alternative decision tree models, such as the gradient-boosting classifier, in differentiating treated cells from their intact counterparts. Despite the methodological challenges associated with fractal analysis and random forest training, this approach offers a promising avenue for the continued exploration of machine learning applications in cellular physiology, pathology, and toxicology.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"286 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135413012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition 具有记忆效应的半无限域中的瞬态热传导:具有Robin边界条件的解析解

2区数学

Fractal and Fractional Pub Date : 2023-10-20 DOI: 10.3390/fractalfract7100770

Vetlugin Dzhabrailovich Beybalaev, Abutrab Aleksandrovich Aliverdiev, Jordan Hristov

引用次数: 0

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications 双极度量空间中的某些插值近端收缩，最佳接近点定理及其应用

2区数学

Fractal and Fractional Pub Date : 2023-10-19 DOI: 10.3390/fractalfract7100766

Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr, Liliana Guran

引用次数: 0

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System 基于分数阶加权混合灵敏度的非线性系统鲁棒控制器设计与应用

2区数学

Fractal and Fractional Pub Date : 2023-10-19 DOI: 10.3390/fractalfract7100769

Erdem Ilten

{"title":"Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System","authors":"Erdem Ilten","doi":"10.3390/fractalfract7100769","DOIUrl":"https://doi.org/10.3390/fractalfract7100769","url":null,"abstract":"This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Equilibrium Problem for the Stochastic Multi-Weighted Urban Public Transportation System with Time Delay: A Graph-Theoretic Method 随机多加权城市公共交通系统时滞均衡问题:图论方法

2区数学

Fractal and Fractional Pub Date : 2023-10-19 DOI: 10.3390/fractalfract7100767

Hui Yang, Chunmei Zhang, Ran Li, Huiling Chen

引用次数: 0

Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration 基于Picard-Thakur迭代的超越函数的Mandelbrot和Julia集

2区数学

Fractal and Fractional Pub Date : 2023-10-19 DOI: 10.3390/fractalfract7100768

Ashish Bhoria, Anju Panwar, Mohammad Sajid

引用次数: 0

Disturbance Rejection-Based Optimal PID Controllers for New 6ISO AVR Systems 基于扰动抑制的新型6ISO AVR系统最优PID控制器

2区数学

Fractal and Fractional Pub Date : 2023-10-18 DOI: 10.3390/fractalfract7100765

Muhyaddin Rawa, Sultan Alghamdi, Martin Calasan, Obaid Aldosari, Ziad M. Ali, Salem Alkhalaf, Mihailo Micev, Shady H. E. Abdel Aleem

{"title":"Disturbance Rejection-Based Optimal PID Controllers for New 6ISO AVR Systems","authors":"Muhyaddin Rawa, Sultan Alghamdi, Martin Calasan, Obaid Aldosari, Ziad M. Ali, Salem Alkhalaf, Mihailo Micev, Shady H. E. Abdel Aleem","doi":"10.3390/fractalfract7100765","DOIUrl":"https://doi.org/10.3390/fractalfract7100765","url":null,"abstract":"In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0