Pub Date : 2024-04-07DOI: 10.3390/fractalfract8040214
Kevser Şimşek, Nisa Özge Önal Tuğrul, K. Karaçuha, Vasil Tabatadze, E. Karaçuha
This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample flights, we propose a novel approach combining deep assessment methodology (DAM) with fractional calculus theory. By modeling the relationship between PLF and the number of days remaining until a flight, our method yields minimal errors compared to traditional techniques. Through a continuous curve constructed using the least-squares approach, we enable the anticipation of future flight values. Our analysis demonstrates that the DAM model with a first-order derivative outperforms linear techniques and the Fractional Model-3 in both modeling capabilities and prediction accuracy. The proposed approach offers a data-driven solution for efficiently managing air transport capacity, with implications for revenue optimization. Specifically, our modeling findings indicate that the DAM wd model improves prediction accuracy by approximately 0.67 times compared to the DAM model, surpassing the fractional model and regression analysis. For the DAM wd modeling method, the lowest average mean absolute percentage error (AMAPE) value achieved is 0.571, showcasing its effectiveness in forecasting flight outcomes.
本研究探讨了如何预测航空运输中的客座率（PLF），以优化运力管理并实现收益最大化。利用土耳其航空公司 19 条市场航线和样本航班的历史预订数据，我们提出了一种将深度评估方法 (DAM) 与分数微积分理论相结合的新方法。通过模拟 PLF 与航班剩余天数之间的关系，我们的方法与传统技术相比误差最小。通过使用最小二乘法构建的连续曲线，我们可以预测未来的航班值。我们的分析表明，带有一阶导数的 DAM 模型在建模能力和预测精度方面均优于线性技术和分数模型-3。所提出的方法为有效管理航空运输能力提供了以数据为导向的解决方案，并对收入优化产生了影响。具体而言，我们的建模结果表明，与 DAM 模型相比，DAM wd 模型的预测精度提高了约 0.67 倍，超过了分数模型和回归分析。DAM wd 建模方法的平均绝对百分比误差（AMAPE）最低值为 0.571，显示了其在预测航班结果方面的有效性。
{"title":"Modeling and Predicting Passenger Load Factor in Air Transportation: A Deep Assessment Methodology with Fractional Calculus Approach Utilizing Reservation Data","authors":"Kevser Şimşek, Nisa Özge Önal Tuğrul, K. Karaçuha, Vasil Tabatadze, E. Karaçuha","doi":"10.3390/fractalfract8040214","DOIUrl":"https://doi.org/10.3390/fractalfract8040214","url":null,"abstract":"This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample flights, we propose a novel approach combining deep assessment methodology (DAM) with fractional calculus theory. By modeling the relationship between PLF and the number of days remaining until a flight, our method yields minimal errors compared to traditional techniques. Through a continuous curve constructed using the least-squares approach, we enable the anticipation of future flight values. Our analysis demonstrates that the DAM model with a first-order derivative outperforms linear techniques and the Fractional Model-3 in both modeling capabilities and prediction accuracy. The proposed approach offers a data-driven solution for efficiently managing air transport capacity, with implications for revenue optimization. Specifically, our modeling findings indicate that the DAM wd model improves prediction accuracy by approximately 0.67 times compared to the DAM model, surpassing the fractional model and regression analysis. For the DAM wd modeling method, the lowest average mean absolute percentage error (AMAPE) value achieved is 0.571, showcasing its effectiveness in forecasting flight outcomes.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140732983","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}
In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.
{"title":"Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals","authors":"Ayrat Zagretdinov, Shamil Ziganshin, Eugenia Izmailova, Yuri Vankov, Ilya Klyukin, Roman Alexandrov","doi":"10.3390/fractalfract8040213","DOIUrl":"https://doi.org/10.3390/fractalfract8040213","url":null,"abstract":"In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140736706","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 : 2024-04-04DOI: 10.3390/fractalfract8040212
Jorge Manuel Barrios-Sánchez, Roberto Baeza-Serrato, L. Martínez-Jiménez
This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the premise of an ideal scenario. In practice, however, accurate models often operate with varying efficiencies due to various irregularities and particularities. This discrepancy is the primary motivation behind our research proposal, which seeks to provide a more realistic understanding of the behavior of the loops, including their different levels of efficiency. To achieve this goal, we propose the introduction of fractional calculus in system dynamics models, focusing specifically on the balancing loops. This innovative approach offers a new perspective on the state of the art, offering new possibilities for understanding and optimizing complex systems.
{"title":"Fractional Calculus to Analyze Efficiency Behavior in a Balancing Loop in a System Dynamics Environment","authors":"Jorge Manuel Barrios-Sánchez, Roberto Baeza-Serrato, L. Martínez-Jiménez","doi":"10.3390/fractalfract8040212","DOIUrl":"https://doi.org/10.3390/fractalfract8040212","url":null,"abstract":"This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the premise of an ideal scenario. In practice, however, accurate models often operate with varying efficiencies due to various irregularities and particularities. This discrepancy is the primary motivation behind our research proposal, which seeks to provide a more realistic understanding of the behavior of the loops, including their different levels of efficiency. To achieve this goal, we propose the introduction of fractional calculus in system dynamics models, focusing specifically on the balancing loops. This innovative approach offers a new perspective on the state of the art, offering new possibilities for understanding and optimizing complex systems.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140743533","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 : 2024-04-04DOI: 10.3390/fractalfract8040211
A. Samadi, Sotiris K. Ntouyas, J. Tariboon
This paper deals with a nonlocal fractional coupled system of (k,ψ)-Hilfer fractional differential equations, which involve, in boundary conditions, (k,ψ)-Hilfer fractional derivatives and (k,ψ)-Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel’skiĭ’s fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples.
{"title":"Study on a Nonlocal Fractional Coupled System Involving (k,ψ)-Hilfer Derivatives and (k,ψ)-Riemann–Liouville Integral Operators","authors":"A. Samadi, Sotiris K. Ntouyas, J. Tariboon","doi":"10.3390/fractalfract8040211","DOIUrl":"https://doi.org/10.3390/fractalfract8040211","url":null,"abstract":"This paper deals with a nonlocal fractional coupled system of (k,ψ)-Hilfer fractional differential equations, which involve, in boundary conditions, (k,ψ)-Hilfer fractional derivatives and (k,ψ)-Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel’skiĭ’s fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140744433","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 : 2024-04-03DOI: 10.3390/fractalfract8040210
Md Ashik Iqbal, A. Ganie, M. M. Miah, M. S. Osman
Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and the time-fractional Clannish Random Walker’s Parabolic equation (CRWPE). These models were investigated by using an expansion method for extracting new soliton solutions. Two types of results were found: one was trigonometric and the other one was an exponential form. For a profound explanation of the physical phenomena of the studied fractional models, some results were graphed in 2D, 3D, and contour plots by imposing the distinctive results for some parameters under the oblige conditions. From the numerical investigation, it was noticed that the obtained results referred smooth kink-shaped soliton, ant-kink-shaped soliton, bright kink-shaped soliton, singular periodic solution, and multiple singular periodic solutions. The results also showed that the amplitude of the wave augmented with the pulsation in time, which derived the order of time fractional coefficient, remarkably enhanced the wave propagation, and influenced the nonlinearity impacts.
{"title":"Extracting the Ultimate New Soliton Solutions of Some Nonlinear Time Fractional PDEs via the Conformable Fractional Derivative","authors":"Md Ashik Iqbal, A. Ganie, M. M. Miah, M. S. Osman","doi":"10.3390/fractalfract8040210","DOIUrl":"https://doi.org/10.3390/fractalfract8040210","url":null,"abstract":"Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and the time-fractional Clannish Random Walker’s Parabolic equation (CRWPE). These models were investigated by using an expansion method for extracting new soliton solutions. Two types of results were found: one was trigonometric and the other one was an exponential form. For a profound explanation of the physical phenomena of the studied fractional models, some results were graphed in 2D, 3D, and contour plots by imposing the distinctive results for some parameters under the oblige conditions. From the numerical investigation, it was noticed that the obtained results referred smooth kink-shaped soliton, ant-kink-shaped soliton, bright kink-shaped soliton, singular periodic solution, and multiple singular periodic solutions. The results also showed that the amplitude of the wave augmented with the pulsation in time, which derived the order of time fractional coefficient, remarkably enhanced the wave propagation, and influenced the nonlinearity impacts.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140747840","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 : 2024-04-03DOI: 10.3390/fractalfract8040209
Binbin Yang, Lichuang Jin
Fractal geometry is a geometry that focuses on irregular geometric forms and can quantitatively describe rough and uneven surfaces and interfaces. As the main material for making natural fiber geotextile, rice straw fiber can reduce the direct impact of rainfall on soil and reduce the intensity of hydraulic erosion. This study investigates whether the use of rice straw fiber as an additive to reinforce arid soil can inhibit moisture evaporation and prevent cracking. Samples with different fiber contents added (0%, 1%, 2%, and 4%) are placed in an environmental chamber to simulate the effects of an arid climatic condition and control the temperature and humidity levels. The cracking process of the samples is recorded by using a digital camera, and the parameters of the evaporation and cracking processes are quantitatively examined through digital image processing. The results show that all of the samples with fiber have a higher residual water content and can retain 31.4%, 58.5%, and 101.9% more water than without the fibers, respectively. Furthermore, both the primary and secondary cracks as well as crack networks are inhibited in samples with a higher fiber content, that is, 2% or 4% fiber contents. The samples reinforced with fiber also have a smaller crack ratio. Compared with the samples without straw fiber, the final crack ratio of the samples with 1%, 2%, and 4% fiber is reduced by 8.05%, 24.09%, and 35.01% respectively. Finally, the final fractal dimensions of the cracks in samples with fiber contents are also reduced by 0.54%, 5.50%, and 6.40% for the samples with 1%, 2%, and 4% fiber, respectively. The addition of natural fiber as an additive to reduce evaporative cracking in soil can: (1) reduce the soil porosity; (2) enhance the binding force between the soil particles; and (3) block the hydrophobic channels. Therefore, the addition of rice straw fiber to soil can effectively reduce soil evaporation and inhibit soil cracking.
{"title":"Fractal Characteristics of Natural Fiber-Reinforced Soil in Arid Climate Due to Cracking","authors":"Binbin Yang, Lichuang Jin","doi":"10.3390/fractalfract8040209","DOIUrl":"https://doi.org/10.3390/fractalfract8040209","url":null,"abstract":"Fractal geometry is a geometry that focuses on irregular geometric forms and can quantitatively describe rough and uneven surfaces and interfaces. As the main material for making natural fiber geotextile, rice straw fiber can reduce the direct impact of rainfall on soil and reduce the intensity of hydraulic erosion. This study investigates whether the use of rice straw fiber as an additive to reinforce arid soil can inhibit moisture evaporation and prevent cracking. Samples with different fiber contents added (0%, 1%, 2%, and 4%) are placed in an environmental chamber to simulate the effects of an arid climatic condition and control the temperature and humidity levels. The cracking process of the samples is recorded by using a digital camera, and the parameters of the evaporation and cracking processes are quantitatively examined through digital image processing. The results show that all of the samples with fiber have a higher residual water content and can retain 31.4%, 58.5%, and 101.9% more water than without the fibers, respectively. Furthermore, both the primary and secondary cracks as well as crack networks are inhibited in samples with a higher fiber content, that is, 2% or 4% fiber contents. The samples reinforced with fiber also have a smaller crack ratio. Compared with the samples without straw fiber, the final crack ratio of the samples with 1%, 2%, and 4% fiber is reduced by 8.05%, 24.09%, and 35.01% respectively. Finally, the final fractal dimensions of the cracks in samples with fiber contents are also reduced by 0.54%, 5.50%, and 6.40% for the samples with 1%, 2%, and 4% fiber, respectively. The addition of natural fiber as an additive to reduce evaporative cracking in soil can: (1) reduce the soil porosity; (2) enhance the binding force between the soil particles; and (3) block the hydrophobic channels. Therefore, the addition of rice straw fiber to soil can effectively reduce soil evaporation and inhibit soil cracking.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140746046","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 : 2024-04-02DOI: 10.3390/fractalfract8040207
Mutum Zico Meetei, Shahbaz Zafar, Abdullah A. Zaagan, Ali M. Mahnashi, Muhammad Idrees
This work presents a quantitative analysis of the transmission dynamics of dengue using the Caputo–Fabrizio fractional-order derivative. It presents an extensive framework for modeling a dengue epidemic, including the various stages of infection and encompassing a wide range of transmission pathways. The proposed model is subjected to a rigorous qualitative study, including the determination of a non-negative solution, the assessment of the basic reproduction number, and an evaluation of local stability. Numerical solutions are obtained using the Newton method. The fractional-order operator, developed using the Caputo–Fabrizio approach, provides a refined perspective on the transmission dynamics of dengue. This study contributes to a deeper understanding of the disease’s transmission mechanisms, considering both fractional-order dynamics and diverse transmission routes, thus offering insights for enhanced disease management and control.
{"title":"Dengue Transmission Dynamics: A Fractional-Order Approach with Compartmental Modeling","authors":"Mutum Zico Meetei, Shahbaz Zafar, Abdullah A. Zaagan, Ali M. Mahnashi, Muhammad Idrees","doi":"10.3390/fractalfract8040207","DOIUrl":"https://doi.org/10.3390/fractalfract8040207","url":null,"abstract":"This work presents a quantitative analysis of the transmission dynamics of dengue using the Caputo–Fabrizio fractional-order derivative. It presents an extensive framework for modeling a dengue epidemic, including the various stages of infection and encompassing a wide range of transmission pathways. The proposed model is subjected to a rigorous qualitative study, including the determination of a non-negative solution, the assessment of the basic reproduction number, and an evaluation of local stability. Numerical solutions are obtained using the Newton method. The fractional-order operator, developed using the Caputo–Fabrizio approach, provides a refined perspective on the transmission dynamics of dengue. This study contributes to a deeper understanding of the disease’s transmission mechanisms, considering both fractional-order dynamics and diverse transmission routes, thus offering insights for enhanced disease management and control.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140755023","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 : 2024-04-02DOI: 10.3390/fractalfract8040208
Nouf Abdulrahman Alqahtani, S. Qaisar, Arslan Munir, Muhammad Naeem, Hüseyin Budak
Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.
{"title":"Error Bounds for Fractional Integral Inequalities with Applications","authors":"Nouf Abdulrahman Alqahtani, S. Qaisar, Arslan Munir, Muhammad Naeem, Hüseyin Budak","doi":"10.3390/fractalfract8040208","DOIUrl":"https://doi.org/10.3390/fractalfract8040208","url":null,"abstract":"Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140753241","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 : 2024-03-22DOI: 10.3390/fractalfract8040181
Fadile Sen, A. Kircay, Buket Sonbas Cobb, A. Akgul
This study introduces an innovative filter topology capable of providing simultaneous positive and negative gain outputs for one-fractional order LP, with high-pass, all-pass, and fractional-order shelving filter responses. The circuit, utilizing multi-output second-generation current-controlled conveyors, stands out as the first to deliver ten outputs, incorporating both integer and fractional-order filter responses, without requiring additional components. Its current-mode design simplifies the process, employing minimal active and grounded passive elements, making it appropriate for low-voltage/low-power applications. The filter utilizes fifth-order Oustaloup approximation and Foster type-I RC networks for fractional-order capacitors, providing enhanced control over the transition slope. PSpice simulations confirmed a 1 kHz cut-off, showcasing low power consumption, minimal noise, and a wide dynamic range, positioning the filter as suitable for sensors, control, and acoustic applications.
{"title":"MO-CCCII-Based Single-Input Multi-Output (SIMO) Current-Mode Fractional-Order Universal and Shelving Filter","authors":"Fadile Sen, A. Kircay, Buket Sonbas Cobb, A. Akgul","doi":"10.3390/fractalfract8040181","DOIUrl":"https://doi.org/10.3390/fractalfract8040181","url":null,"abstract":"This study introduces an innovative filter topology capable of providing simultaneous positive and negative gain outputs for one-fractional order LP, with high-pass, all-pass, and fractional-order shelving filter responses. The circuit, utilizing multi-output second-generation current-controlled conveyors, stands out as the first to deliver ten outputs, incorporating both integer and fractional-order filter responses, without requiring additional components. Its current-mode design simplifies the process, employing minimal active and grounded passive elements, making it appropriate for low-voltage/low-power applications. The filter utilizes fifth-order Oustaloup approximation and Foster type-I RC networks for fractional-order capacitors, providing enhanced control over the transition slope. PSpice simulations confirmed a 1 kHz cut-off, showcasing low power consumption, minimal noise, and a wide dynamic range, positioning the filter as suitable for sensors, control, and acoustic applications.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140214392","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 : 2024-03-22DOI: 10.3390/fractalfract8040182
A. Abouelregal, Yazeed Alhassan, Hashem Althagafi, Faisal Alsharif
This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.
{"title":"A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties","authors":"A. Abouelregal, Yazeed Alhassan, Hashem Althagafi, Faisal Alsharif","doi":"10.3390/fractalfract8040182","DOIUrl":"https://doi.org/10.3390/fractalfract8040182","url":null,"abstract":"This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140220044","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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