Pub Date : 2024-04-17DOI: 10.3390/fractalfract8040236
S. Etemad, Sotiris K. Ntouyas, I. Stamova, J. Tariboon
Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p;q)-difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p;q)-operators in this regard. Application of the fixed points of the ρ-θ-contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p;q)-difference Navier problems.
{"title":"On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam","authors":"S. Etemad, Sotiris K. Ntouyas, I. Stamova, J. Tariboon","doi":"10.3390/fractalfract8040236","DOIUrl":"https://doi.org/10.3390/fractalfract8040236","url":null,"abstract":"Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p;q)-difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p;q)-operators in this regard. Application of the fixed points of the ρ-θ-contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p;q)-difference Navier problems.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140693107","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}
Pub Date : 2024-04-16DOI: 10.3390/fractalfract8040232
Qing Li, Hongxia Liu, Wencai Zhao, Xinzhu Meng
In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.
{"title":"Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model","authors":"Qing Li, Hongxia Liu, Wencai Zhao, Xinzhu Meng","doi":"10.3390/fractalfract8040232","DOIUrl":"https://doi.org/10.3390/fractalfract8040232","url":null,"abstract":"In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140694936","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}
Pub Date : 2024-04-16DOI: 10.3390/fractalfract8040233
G. Oros, G. Oros
Fractional calculus has had a powerful impact on recent research, with many applications in different branches of science and engineering [...]
分式微积分对近年来的研究产生了巨大的影响，在科学和工程学的不同分支中有许多应用 [...]
{"title":"Fractional Calculus and Hypergeometric Functions in Complex Analysis","authors":"G. Oros, G. Oros","doi":"10.3390/fractalfract8040233","DOIUrl":"https://doi.org/10.3390/fractalfract8040233","url":null,"abstract":"Fractional calculus has had a powerful impact on recent research, with many applications in different branches of science and engineering [...]","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140696178","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}
Pub Date : 2024-04-16DOI: 10.3390/fractalfract8040234
Vassilis Alimisis, Nikolaos P. Eleftheriou, Evangelos Georgakilas, Christos Dimas, N. Uzunoglu, P. Sotiriadis
This paper introduces an analog integrated fractional order type-2 fuzzy PID control system. Current approaches frequently depend on energy-intensive embedded digital systems, consuming substantial energy levels ranging from a few μW to mW. To address this limitation we propose a fully analog design offering insights into the potential of analog circuits for powerefficient robust control in complex and uncertain environments. It consists of Gaussian function, min/max, Operational transcoductance amplifier circuits and Resistor-Capacitor networks for the implementation of the fractional-order components. Crafted for operation under a reduced voltage supply (0.6 V), the controller attains minimal power usage (861.8 nW), facilitating uninterrupted, extended-term functioning. Post-layout simulation results confirm the proper operation of the proposed design. The proposed system is designed and simulated using the Cadence IC Suite in a TSMC 90 nm CMOS process.
本文介绍了一种模拟集成分数阶 2 型模糊 PID 控制系统。目前的方法通常依赖于高能耗的嵌入式数字系统，能耗水平从几微瓦到几毫瓦不等。为解决这一局限性，我们提出了一种全模拟设计方案，让人们深入了解模拟电路在复杂和不确定环境下实现高能效稳健控制的潜力。它由高斯函数、最小/最大、运算跨导放大器电路和用于实现分数阶组件的电阻电容网络组成。该控制器可在电压较低的电源（0.6 V）下运行，功耗极低（861.8 nW），有利于不间断地长期运行。布局后仿真结果证实了拟议设计的正常运行。该系统采用 Cadence IC Suite 在台积电 90 纳米 CMOS 工艺中进行设计和仿真。
{"title":"A Low Power Analog Integrated Fractional Order Type-2 Fuzzy PID Controller","authors":"Vassilis Alimisis, Nikolaos P. Eleftheriou, Evangelos Georgakilas, Christos Dimas, N. Uzunoglu, P. Sotiriadis","doi":"10.3390/fractalfract8040234","DOIUrl":"https://doi.org/10.3390/fractalfract8040234","url":null,"abstract":"This paper introduces an analog integrated fractional order type-2 fuzzy PID control system. Current approaches frequently depend on energy-intensive embedded digital systems, consuming substantial energy levels ranging from a few μW to mW. To address this limitation we propose a fully analog design offering insights into the potential of analog circuits for powerefficient robust control in complex and uncertain environments. It consists of Gaussian function, min/max, Operational transcoductance amplifier circuits and Resistor-Capacitor networks for the implementation of the fractional-order components. Crafted for operation under a reduced voltage supply (0.6 V), the controller attains minimal power usage (861.8 nW), facilitating uninterrupted, extended-term functioning. Post-layout simulation results confirm the proper operation of the proposed design. The proposed system is designed and simulated using the Cadence IC Suite in a TSMC 90 nm CMOS process.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140696857","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}
Pub Date : 2024-04-16DOI: 10.3390/fractalfract8040230
Areej A. Almoneef, M. Barakat, Abd-Allah Hyder
This work investigates novel fractional Hadamard integral inequalities by utilizing extended convex functions and generalized Riemann-Liouville operators. By carefully using extended integral formulations, we not only find novel inequalities but also improve the accuracy of error bounds related to fractional Hadamard integrals. Our study broadens the applicability of these inequalities and shows that they are useful for a variety of convexity cases. Our results contribute to the advancement of mathematical analysis and provide useful information for theoretical comprehension as well as practical applications across several scientific directions.
{"title":"Further Fractional Hadamard Integral Inequalities Utilizing Extended Convex Functions","authors":"Areej A. Almoneef, M. Barakat, Abd-Allah Hyder","doi":"10.3390/fractalfract8040230","DOIUrl":"https://doi.org/10.3390/fractalfract8040230","url":null,"abstract":"This work investigates novel fractional Hadamard integral inequalities by utilizing extended convex functions and generalized Riemann-Liouville operators. By carefully using extended integral formulations, we not only find novel inequalities but also improve the accuracy of error bounds related to fractional Hadamard integrals. Our study broadens the applicability of these inequalities and shows that they are useful for a variety of convexity cases. Our results contribute to the advancement of mathematical analysis and provide useful information for theoretical comprehension as well as practical applications across several scientific directions.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140698446","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}
Pub Date : 2024-04-16DOI: 10.3390/fractalfract8040231
M. Turkyilmazoglu, A. S. Alofi
This paper applies fractional calculus to a practical example in fluid mechanics, illustrating its impact beyond traditional integer order calculus. We focus on the classic problem of a rigid body rotating within a uniformly rotating container, which generates a liquid vortex from an undisturbed initial state. Our aim is to compare the time evolutions of the physical system in fractional and integer order models by examining the torque transmission from the rotating body to the surrounding liquid. This is achieved through closed-form, time-developing solutions expressed in terms of Mittag–Leffler and Bessel functions. Analysis reveals that the rotational velocity and, consequently, the vortex structure of the liquid are influenced by three distinct time zones that differ between integer and noninteger models. Anomalous diffusion, favoring noninteger fractions, dominates at early times but gradually gives way to the integer derivative model behavior as time progresses through a transitional regime. Our derived vortex formula clearly demonstrates how the liquid vortex is regulated in time for each considered fractional model.
{"title":"Liquid Vortex Formation in a Swirling Container Considering Fractional Time Derivative of Caputo","authors":"M. Turkyilmazoglu, A. S. Alofi","doi":"10.3390/fractalfract8040231","DOIUrl":"https://doi.org/10.3390/fractalfract8040231","url":null,"abstract":"This paper applies fractional calculus to a practical example in fluid mechanics, illustrating its impact beyond traditional integer order calculus. We focus on the classic problem of a rigid body rotating within a uniformly rotating container, which generates a liquid vortex from an undisturbed initial state. Our aim is to compare the time evolutions of the physical system in fractional and integer order models by examining the torque transmission from the rotating body to the surrounding liquid. This is achieved through closed-form, time-developing solutions expressed in terms of Mittag–Leffler and Bessel functions. Analysis reveals that the rotational velocity and, consequently, the vortex structure of the liquid are influenced by three distinct time zones that differ between integer and noninteger models. Anomalous diffusion, favoring noninteger fractions, dominates at early times but gradually gives way to the integer derivative model behavior as time progresses through a transitional regime. Our derived vortex formula clearly demonstrates how the liquid vortex is regulated in time for each considered fractional model.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140697268","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}
Pub Date : 2024-04-15DOI: 10.3390/fractalfract8040226
Andrés J. Serrano-Balbontín, I. Tejado, B. Vinagre
Silicon neurons are bioinspired circuits with the capability to reproduce the modulation through pulse-frequency observed in real neurons. They are of particular interest in closed-loop schemes to encode the control signal into pulses. This paper proposes the analog realization of neuromorphic silicon neurons with fractional dynamics. In particular, the fractional-order (FO) operator is introduced into classical neurons with the intention of reproducing the adaptation that has been observed experimentally in real neurons, which is the variation in the firing frequency even when considering a constant or periodic incoming stimulus. For validation purposes, simulations using a field-programmable analog array (FPAA) are performed to verify the behavior of the circuits.
{"title":"Field-Programmable Analog Array Implementation of Neuromorphic Silicon Neurons with Fractional Dynamics","authors":"Andrés J. Serrano-Balbontín, I. Tejado, B. Vinagre","doi":"10.3390/fractalfract8040226","DOIUrl":"https://doi.org/10.3390/fractalfract8040226","url":null,"abstract":"Silicon neurons are bioinspired circuits with the capability to reproduce the modulation through pulse-frequency observed in real neurons. They are of particular interest in closed-loop schemes to encode the control signal into pulses. This paper proposes the analog realization of neuromorphic silicon neurons with fractional dynamics. In particular, the fractional-order (FO) operator is introduced into classical neurons with the intention of reproducing the adaptation that has been observed experimentally in real neurons, which is the variation in the firing frequency even when considering a constant or periodic incoming stimulus. For validation purposes, simulations using a field-programmable analog array (FPAA) are performed to verify the behavior of the circuits.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140703704","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}
Pub Date : 2024-04-15DOI: 10.3390/fractalfract8040228
Feng Cai, Qian Zhang, Lingling Yang
The degree of irregularity and complexity of the pore structure are comprehensively reflected in the fractal dimension. The porosity of coal was determined by its fractal dimension, where a larger dimension indicates a lower porosity. Fractal theory and the Frenkel–Halsey–Hill (FHH) model were applied to explore the variation rules of concentration on functional groups and pore structure in this study. Combined with infrared spectroscopy (FTIR) and low-temperature nitrogen adsorption, a starch-polymerized aluminum sulfate composite fracturing fluid was prepared, which plays an important role in methane adsorption and permeability of coal samples. The test results showed that, compared with the original coal, the pore volume and specific surface area of each group of coal samples were reduced, the average pore diameter was initially enlarged and then declined, and fractal dimension D1 dropped by 5.4% to 15.4%, while fractal dimension D2 gained 1.2% to 7.9%. Moreover, the nitrogen adsorption of each group of coal samples was obviously lower than the original coal, and the concentration of starch-polymerized aluminum sulfate solution existed at a critical optimal concentration for the modification of the coal samples, and the nitrogen adsorption reached a minimum value of 0.6814 cm3/g at a concentration of 10%. The novel composite solution prepared by the combination of starch and flocculant in this paper enhanced the permeability of the coal seam, which is of great significance in improving the efficiency of coalbed methane mining.
{"title":"Fractal Characteristics and Microstructure of Coal with Impact of Starch-Polymerized Aluminum Sulfate Fracturing Fluids","authors":"Feng Cai, Qian Zhang, Lingling Yang","doi":"10.3390/fractalfract8040228","DOIUrl":"https://doi.org/10.3390/fractalfract8040228","url":null,"abstract":"The degree of irregularity and complexity of the pore structure are comprehensively reflected in the fractal dimension. The porosity of coal was determined by its fractal dimension, where a larger dimension indicates a lower porosity. Fractal theory and the Frenkel–Halsey–Hill (FHH) model were applied to explore the variation rules of concentration on functional groups and pore structure in this study. Combined with infrared spectroscopy (FTIR) and low-temperature nitrogen adsorption, a starch-polymerized aluminum sulfate composite fracturing fluid was prepared, which plays an important role in methane adsorption and permeability of coal samples. The test results showed that, compared with the original coal, the pore volume and specific surface area of each group of coal samples were reduced, the average pore diameter was initially enlarged and then declined, and fractal dimension D1 dropped by 5.4% to 15.4%, while fractal dimension D2 gained 1.2% to 7.9%. Moreover, the nitrogen adsorption of each group of coal samples was obviously lower than the original coal, and the concentration of starch-polymerized aluminum sulfate solution existed at a critical optimal concentration for the modification of the coal samples, and the nitrogen adsorption reached a minimum value of 0.6814 cm3/g at a concentration of 10%. The novel composite solution prepared by the combination of starch and flocculant in this paper enhanced the permeability of the coal seam, which is of great significance in improving the efficiency of coalbed methane mining.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140701519","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}
Pub Date : 2024-04-15DOI: 10.3390/fractalfract8040229
Yunzhang Zhang, Changjin Xu
In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks.
{"title":"Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay","authors":"Yunzhang Zhang, Changjin Xu","doi":"10.3390/fractalfract8040229","DOIUrl":"https://doi.org/10.3390/fractalfract8040229","url":null,"abstract":"In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140702265","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}
Pub Date : 2024-04-13DOI: 10.3390/fractalfract8040225
Abdul Wadood, Ejaz Ahmed, Sang Bong Rhee, Babar Sattar Khan
This research utilizes the innovative fractional-order Archimedean spiral moth–flame optimization (FO-AMFO) technique to address the issues of the optimal reactive power dispatch (ORPD) problem. The formulated fitness function aims to minimize power losses and determine the ideal flow of reactive power for the IEEE 30- and 57-bus test systems. The extensive functions of the fractional evolutionary computing strategy are utilized to address the minimization problem of ORPD. This involves determining the control variables, such as VAR compensators, bus voltages, and the tap setting of the transformers. The effective incorporation of reactive compensation devices into traditional power grids has greatly reduced power losses; however, it has resulted in an increase in the complexity of optimization problems. A comparison of the findings indicates that swarming fractional intelligence using FO-AMFO surpassed the state-of-the-art competitors in terms of minimizing power losses.
{"title":"A Fractional-Order Archimedean Spiral Moth–Flame Optimization Strategy to Solve Optimal Power Flows","authors":"Abdul Wadood, Ejaz Ahmed, Sang Bong Rhee, Babar Sattar Khan","doi":"10.3390/fractalfract8040225","DOIUrl":"https://doi.org/10.3390/fractalfract8040225","url":null,"abstract":"This research utilizes the innovative fractional-order Archimedean spiral moth–flame optimization (FO-AMFO) technique to address the issues of the optimal reactive power dispatch (ORPD) problem. The formulated fitness function aims to minimize power losses and determine the ideal flow of reactive power for the IEEE 30- and 57-bus test systems. The extensive functions of the fractional evolutionary computing strategy are utilized to address the minimization problem of ORPD. This involves determining the control variables, such as VAR compensators, bus voltages, and the tap setting of the transformers. The effective incorporation of reactive compensation devices into traditional power grids has greatly reduced power losses; however, it has resulted in an increase in the complexity of optimization problems. A comparison of the findings indicates that swarming fractional intelligence using FO-AMFO surpassed the state-of-the-art competitors in terms of minimizing power losses.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140706878","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}
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