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Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators 雷纳分式算子的哈达玛德积分不等式的新估算方法
Fractal and Fractional Pub Date : 2024-05-20 DOI: 10.3390/fractalfract8050302
Merve Coşkun, Çetin Yıldız, Luminița-Ioana Cotîrlă
{"title":"Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators","authors":"Merve Coşkun, Çetin Yıldız, Luminița-Ioana Cotîrlă","doi":"10.3390/fractalfract8050302","DOIUrl":"https://doi.org/10.3390/fractalfract8050302","url":null,"abstract":"In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"26 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis 揭示艾滋病毒传播的复杂性：通过分形-分形分析整合多级感染
Fractal and Fractional Pub Date : 2024-05-20 DOI: 10.3390/fractalfract8050299
Yasir Nadeem Anjam, Rubayyi Turki Alqahtani, N. Alharthi, Saira Tabassum
{"title":"Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis","authors":"Yasir Nadeem Anjam, Rubayyi Turki Alqahtani, N. Alharthi, Saira Tabassum","doi":"10.3390/fractalfract8050299","DOIUrl":"https://doi.org/10.3390/fractalfract8050299","url":null,"abstract":"This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"25 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Augmenting the Stability of Automatic Voltage Regulators through Sophisticated Fractional-Order Controllers 通过先进的分数阶控制器增强自动电压调节器的稳定性
Fractal and Fractional Pub Date : 2024-05-20 DOI: 10.3390/fractalfract8050300
Emad A. Mohamed, M. Aly, W. Alhosaini, Emad M. Ahmed
{"title":"Augmenting the Stability of Automatic Voltage Regulators through Sophisticated Fractional-Order Controllers","authors":"Emad A. Mohamed, M. Aly, W. Alhosaini, Emad M. Ahmed","doi":"10.3390/fractalfract8050300","DOIUrl":"https://doi.org/10.3390/fractalfract8050300","url":null,"abstract":"The transition from traditional to renewable energy sources is a critical issue in current energy-generation systems, which aims to address climate change and the increased demand for energy. This shift, however, imposes additional burdens on control systems to maintain power system stability and quality within predefined limits. Addressing these challenges, this paper proposes an innovative Modified Hybrid Fractional-Order (MHFO) automatic voltage regulator (AVR) equipped with a fractional-order tilt integral and proportional derivative with a filter plus a second-order derivative with a filter FOTI-PDND2N2 controller. This advanced controller combines the benefits of a (FOTI) controller, known for enhancing dynamic performance and steady-state response, with a (PDND2N2) controller to improve system robustness and adaptability. The proposed MHFO controller stands out with its nine tunable parameters, providing more extensive control options than the conventional three-parameter PID controller and the five-parameter FOPID controller. Furthermore, a recent optimization approach using a growth optimizer (GO) has been formulated and applied to optimally adjust the MHFO controller’s parameters simultaneously. The performance of the proposed AVR based on the MHFO-GO controller is scrutinized by contrasting it with various established and developed optimization algorithms. The comparative study shows that the AVR based on the MHFO-GO controller surpasses other AVR controllers from the stability, robustness, and dynamic response speed points of view.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141123095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control 通过混合开环反馈控制和脉冲控制实现具有多重延迟的卡普托分数阶不确定膜神经网络的时变函数矩阵投影同步化
Fractal and Fractional Pub Date : 2024-05-20 DOI: 10.3390/fractalfract8050301
Hongguang Fan, Yue Rao, Kaibo Shi, Hui Wen
{"title":"Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control","authors":"Hongguang Fan, Yue Rao, Kaibo Shi, Hui Wen","doi":"10.3390/fractalfract8050301","DOIUrl":"https://doi.org/10.3390/fractalfract8050301","url":null,"abstract":"This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"88 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints 具有非整体约束条件的分数拉格朗日系统的赫格洛茨式诺特定理
Fractal and Fractional Pub Date : 2024-05-18 DOI: 10.3390/fractalfract8050296
Yuanyuan Deng, Yi Zhang
{"title":"Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints","authors":"Yuanyuan Deng, Yi Zhang","doi":"10.3390/fractalfract8050296","DOIUrl":"https://doi.org/10.3390/fractalfract8050296","url":null,"abstract":"This research aims to investigate the Noether symmetry and conserved quantity for the fractional Lagrange system with nonholonomic constraints, which are based on the Herglotz principle. Firstly, the fractional-order Herglotz principle is given, and the Herglotz-type fractional-order differential equations of motion for the fractional Lagrange system with nonholonomic constraints are derived. Secondly, by introducing infinitesimal generating functions of space and time, the Noether symmetry of the Herglotz type is defined, along with its criteria, and the conserved quantity of the Herglotz type is given. Finally, to demonstrate how to use this method, two examples are provided.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"109 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller 通过基于事件的混合脉冲控制器同步具有跳跃错配的分数延迟记忆神经网络
Fractal and Fractional Pub Date : 2024-05-18 DOI: 10.3390/fractalfract8050297
Huiyu Wang, Shutang Liu, Xiang Wu, Jie Sun, W. Qiao
{"title":"Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller","authors":"Huiyu Wang, Shutang Liu, Xiang Wu, Jie Sun, W. Qiao","doi":"10.3390/fractalfract8050297","DOIUrl":"https://doi.org/10.3390/fractalfract8050297","url":null,"abstract":"This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"117 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exploring the Exact Solution of the Space-Fractional Stochastic Regularized Long Wave Equation: A Bifurcation Approach 探索空间-分数随机正则化长波方程的精确解：分岔方法
Fractal and Fractional Pub Date : 2024-05-18 DOI: 10.3390/fractalfract8050298
Bashayr Almutairi, M. Al Nuwairan, Anwar Aldhafeeri
{"title":"Exploring the Exact Solution of the Space-Fractional Stochastic Regularized Long Wave Equation: A Bifurcation Approach","authors":"Bashayr Almutairi, M. Al Nuwairan, Anwar Aldhafeeri","doi":"10.3390/fractalfract8050298","DOIUrl":"https://doi.org/10.3390/fractalfract8050298","url":null,"abstract":"This study explores the effects of using space-fractional derivatives and adding multiplicative noise, modeled by a Wiener process, on the solutions of the space-fractional stochastic regularized long wave equation. New fractional stochastic solutions are constructed, and the consistency of the obtained solutions is examined using the transition between phase plane orbits. Their bifurcation and dependence on initial conditions are investigated. Some of these solutions are shown graphically, illustrating both the individual and combined influences of fractional order and noise on selected solutions. These effects appear as alterations in the amplitude and width of the solutions, and as variations in their smoothness.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"114 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders 具有不同阶数的里兹空间分式衍生物的扩展戴维-斯图瓦特森系统守恒原理的理论研究
Fractal and Fractional Pub Date : 2024-03-31 DOI: 10.3390/fractalfract8040206
Carlos Alberto Molina-Holguín, E. Urenda-Cázares, J. Macías-Díaz, Armando Gallegos
{"title":"Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders","authors":"Carlos Alberto Molina-Holguín, E. Urenda-Cázares, J. Macías-Díaz, Armando Gallegos","doi":"10.3390/fractalfract8040206","DOIUrl":"https://doi.org/10.3390/fractalfract8040206","url":null,"abstract":"In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractional-case scenario. In this work, we will prove rigorously that these functionals are conserved throughout time using some functional properties of the Riesz fractional operators. This study is intended to serve as a stepping stone for further exploration of the generalized Davey–Stewartson system and its wide-ranging applications.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"38 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140358204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fractal Properties of Composite-Modified Carbon Paste Electrodes—A Comparison between SEM and CV Fractal Analysis 复合材料改性碳浆电极的分形特性--SEM 与 CV 分形分析的比较
Fractal and Fractional Pub Date : 2024-03-31 DOI: 10.3390/fractalfract8040205
G. Dobrescu, Ramona Georgescu-State, F. Papa, Jacobus (Koos) Frederick van Staden, R. State
{"title":"Fractal Properties of Composite-Modified Carbon Paste Electrodes—A Comparison between SEM and CV Fractal Analysis","authors":"G. Dobrescu, Ramona Georgescu-State, F. Papa, Jacobus (Koos) Frederick van Staden, R. State","doi":"10.3390/fractalfract8040205","DOIUrl":"https://doi.org/10.3390/fractalfract8040205","url":null,"abstract":"The fractal properties of carbon paste electrodes (CPEs) and carbon paste electrodes modified with ionic liquid (IL), AuTiO2/graphene oxide, and IL/AuTiO2/graphene oxide were investigated using scanning electron microscopy (SEM), and cyclic voltammetry (CV). The impact of fractal dimensions and self-similarity ranges on electrochemical responses was underlined. It was proved that a higher fractal dimension and a broad self-similarity domain lead to a higher electrochemical response. Results indicated that IL/AuTiO2/graphene oxide composite-modified CPEs are a great candidate to be used as electrochemical sensors, with a high fractal dimension and large self-similarity domain.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140360455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms 具有规则和不规则节奏的循环信号建模问题中的循环随机过程同构多维结构
Fractal and Fractional Pub Date : 2024-03-30 DOI: 10.3390/fractalfract8040203
Serhii Lupenko, Roman Butsiy
{"title":"Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms","authors":"Serhii Lupenko, Roman Butsiy","doi":"10.3390/fractalfract8040203","DOIUrl":"https://doi.org/10.3390/fractalfract8040203","url":null,"abstract":"This paper is devoted to the research of the isomorphic multidimensional cyclic structure and multidimensional phase structure of the cyclic random process (CRP) and to its formation method, which enables a rigorous formalization of intuitive ideas concerning cyclic stochastic motion. The fundamental properties of the cyclic random process and analytical dependencies between the multidimensional cyclic structure, multidimensional phase structure and rhythm structure of the CRP have been established. This work shows that the CRP is able to take into account the cyclicity of multidimensional distribution functions of cyclic signals as well as the variability in the rhythm of the investigated signals. A subclass of the CRP is the periodic random process, which allows for the use of classical processing methods of cyclic signals with a regular rhythm. Based on a series of experiments, significant advantages of the CRP as a mathematical model of electrocardiographic signals (ECG) compared to the periodic random process are shown.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140362433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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