Pub Date : 2024-03-22DOI: 10.3390/fractalfract8040180
Asifa Tassaddiq, R. Srivastava, Rabab Alharbi, R. Kasmani, Sania Qureshi
The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to establish Minkowski fractional inequalities. Several other new and novel fractional integral inequalities are also established. Compared to the existing results, these fractional integral inequalities are more general and substantial enough to create new and novel results. M-E-K fractional integral operators have been previously applied for other purposes but have never been applied to the subject of this paper. These operators generalize a popular class of fractional integrals; therefore, this approach will open an avenue for new research. The smart properties of these operators urge us to investigate more results using them.
{"title":"New Inequalities Using Multiple Erdélyi–Kober Fractional Integral Operators","authors":"Asifa Tassaddiq, R. Srivastava, Rabab Alharbi, R. Kasmani, Sania Qureshi","doi":"10.3390/fractalfract8040180","DOIUrl":"https://doi.org/10.3390/fractalfract8040180","url":null,"abstract":"The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to establish Minkowski fractional inequalities. Several other new and novel fractional integral inequalities are also established. Compared to the existing results, these fractional integral inequalities are more general and substantial enough to create new and novel results. M-E-K fractional integral operators have been previously applied for other purposes but have never been applied to the subject of this paper. These operators generalize a popular class of fractional integrals; therefore, this approach will open an avenue for new research. The smart properties of these operators urge us to investigate more results using them.","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":"140211906","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/fractalfract8040179
Qi Yang, Yilu Wang, Lu Liu, Xiaomeng Zhang
We propose an adaptive fractional multi-scale optimization optical flow algorithm, which for the first time improves the over-smoothing of optical flow estimation under the total variation model from the perspective of global feature and local texture balance, and solves the problem that the convergence of fractional optical flow algorithms depends on the order parameter. Specifically, a fractional-order discrete L1-regularization Total Variational Optical Flow model is constructed. On this basis, the Ant Lion algorithm is innovatively used to realize the iterative calculation of the optical flow equation, and the fractional order is dynamically adjusted to obtain an adaptive optimization algorithm with strong search accuracy and high efficiency. In this paper, the flexibility of optical flow estimation in weak gradient texture scenes is increased, and the optical flow extraction rate of target features at multiple scales is greatly improved. We show excellent recognition performance and stability under the MPI_Sintel and Middlebury benchmarks.
{"title":"Adaptive Fractional-Order Multi-Scale Optimization TV-L1 Optical Flow Algorithm","authors":"Qi Yang, Yilu Wang, Lu Liu, Xiaomeng Zhang","doi":"10.3390/fractalfract8040179","DOIUrl":"https://doi.org/10.3390/fractalfract8040179","url":null,"abstract":"We propose an adaptive fractional multi-scale optimization optical flow algorithm, which for the first time improves the over-smoothing of optical flow estimation under the total variation model from the perspective of global feature and local texture balance, and solves the problem that the convergence of fractional optical flow algorithms depends on the order parameter. Specifically, a fractional-order discrete L1-regularization Total Variational Optical Flow model is constructed. On this basis, the Ant Lion algorithm is innovatively used to realize the iterative calculation of the optical flow equation, and the fractional order is dynamically adjusted to obtain an adaptive optimization algorithm with strong search accuracy and high efficiency. In this paper, the flexibility of optical flow estimation in weak gradient texture scenes is increased, and the optical flow extraction rate of target features at multiple scales is greatly improved. We show excellent recognition performance and stability under the MPI_Sintel and Middlebury benchmarks.","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":"140217598","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 : 2024-03-21DOI: 10.3390/fractalfract8030178
Obaid J. Algahtani
This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order α modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented.
{"title":"Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System","authors":"Obaid J. Algahtani","doi":"10.3390/fractalfract8030178","DOIUrl":"https://doi.org/10.3390/fractalfract8030178","url":null,"abstract":"This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order α modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140221089","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 : 2024-03-19DOI: 10.3390/fractalfract8030177
Jinshan Liu, Huanhe Dong, Yong Fang, Yong Zhang
The Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four nonlocal equations, we utilize the Riemann–Hilbert method. Compared to the local HOGI equation, the solutions of nonlocal equations not only depend on the local spatial and time variables, but also the nonlocal variables. To exhibit the dynamic behavior, we consider the reverse-spacetime multi-component HOGI equation and its Riemann–Hilbert problem. When the Riemann–Hilbert problem is regular, the integral form solution can be given. Conversely, the exact solutions can be obtained explicitly. Finally, as concrete examples, the periodic solutions of the two-component nonlocal HOGI equation are given, which is different from the local equation.
{"title":"The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem","authors":"Jinshan Liu, Huanhe Dong, Yong Fang, Yong Zhang","doi":"10.3390/fractalfract8030177","DOIUrl":"https://doi.org/10.3390/fractalfract8030177","url":null,"abstract":"The Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four nonlocal equations, we utilize the Riemann–Hilbert method. Compared to the local HOGI equation, the solutions of nonlocal equations not only depend on the local spatial and time variables, but also the nonlocal variables. To exhibit the dynamic behavior, we consider the reverse-spacetime multi-component HOGI equation and its Riemann–Hilbert problem. When the Riemann–Hilbert problem is regular, the integral form solution can be given. Conversely, the exact solutions can be obtained explicitly. Finally, as concrete examples, the periodic solutions of the two-component nonlocal HOGI equation are given, which is different from the local equation.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140230321","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 : 2024-03-19DOI: 10.3390/fractalfract8030176
Benjamin Ducharne, H. Hamzehbahmani, Yanhui Gao, P. Fagan, G. Sebald
Grain-oriented silicon steel (GO FeSi) laminations are vital components for efficient energy conversion in electromagnetic devices. While traditionally optimized for power frequencies of 50/60 Hz, the pursuit of higher frequency operation (f ≥ 200 Hz) promises enhanced power density. This paper introduces a model for estimating GO FeSi laminations’ magnetic behavior under these elevated operational frequencies. The proposed model combines the Maxwell diffusion equation and a material law derived from a fractional differential equation, capturing the viscoelastic characteristics of the magnetization process. Remarkably, the model’s dynamical contribution, characterized by only two parameters, achieves a notable 4.8% Euclidean relative distance error across the frequency spectrum from 50 Hz to 1 kHz. The paper’s initial section offers an exhaustive description of the model, featuring comprehensive comparisons between simulated and measured data. Subsequently, a methodology is presented for the localized segregation of magnetic losses into three conventional categories: hysteresis, classical, and excess, delineated across various tested frequencies. Further leveraging the model’s predictive capabilities, the study extends to investigating the very high-frequency regime, elucidating the spatial distribution of loss contributions. The application of proportional–iterative learning control facilitates the model’s adaptation to standard characterization conditions, employing sinusoidal imposed flux density. The paper deliberates on the implications of GO FeSi behavior under extreme operational conditions, offering insights and reflections essential for understanding and optimizing magnetic core performance in high-frequency applications.
{"title":"High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination","authors":"Benjamin Ducharne, H. Hamzehbahmani, Yanhui Gao, P. Fagan, G. Sebald","doi":"10.3390/fractalfract8030176","DOIUrl":"https://doi.org/10.3390/fractalfract8030176","url":null,"abstract":"Grain-oriented silicon steel (GO FeSi) laminations are vital components for efficient energy conversion in electromagnetic devices. While traditionally optimized for power frequencies of 50/60 Hz, the pursuit of higher frequency operation (f ≥ 200 Hz) promises enhanced power density. This paper introduces a model for estimating GO FeSi laminations’ magnetic behavior under these elevated operational frequencies. The proposed model combines the Maxwell diffusion equation and a material law derived from a fractional differential equation, capturing the viscoelastic characteristics of the magnetization process. Remarkably, the model’s dynamical contribution, characterized by only two parameters, achieves a notable 4.8% Euclidean relative distance error across the frequency spectrum from 50 Hz to 1 kHz. The paper’s initial section offers an exhaustive description of the model, featuring comprehensive comparisons between simulated and measured data. Subsequently, a methodology is presented for the localized segregation of magnetic losses into three conventional categories: hysteresis, classical, and excess, delineated across various tested frequencies. Further leveraging the model’s predictive capabilities, the study extends to investigating the very high-frequency regime, elucidating the spatial distribution of loss contributions. The application of proportional–iterative learning control facilitates the model’s adaptation to standard characterization conditions, employing sinusoidal imposed flux density. The paper deliberates on the implications of GO FeSi behavior under extreme operational conditions, offering insights and reflections essential for understanding and optimizing magnetic core performance in high-frequency applications.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228447","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 : 2024-03-18DOI: 10.3390/fractalfract8030175
N. Bauman, J. Srbljanović, Ivana Čolović Čalovski, Olivera Lijeskić, V. Ćirković, Jelena Trajković, B. Bobić, Andjelija Ž. Ilić, T. Štajner
Toxoplasma gondii is an obligate intracellular parasite existing in three infectious life stages—tachyzoites, bradyzoites, and sporozoites. Rupture of tissue cysts and re-conversion of bradyzoites to tachyzoites leads to reactivated toxoplasmosis (RT) in an immunocompromised host. The aim of this study was to apply ImageJ software for analysis of T. gondii brain cysts obtained from a newly established in vivo model of RT. Mice chronically infected with T. gondii (BGD1 and BGD26 strains) were treated with cyclophosphamide and hydrocortisone (experimental group—EG) or left untreated as infection controls (ICs). RT in mice was confirmed by qPCR (PCR+); mice remaining chronically infected were PCR−. A total of 90 images of cysts were analyzed for fractal dimension (FD), lacunarity (L), diameter (D), circularity (C), and packing density (PD). Circularity was significantly higher in PCR+ compared to IC mice (p < 0.05 for BGD1, p < 0.001 for the BGD26 strain). A significant negative correlation between D and PD was observed only in IC for the BGD1 strain (ρ = −0.384, p = 0.048), while fractal parameters were stable. Significantly higher D, C, and PD and lower lacunarity, L, were noticed in the BGD1 compared to the more aggressive BGD26 strain. In conclusion, these results demonstrate the complexity of structural alterations of T. gondii cysts in an immunocompromised host and emphasize the application potential of ImageJ in the experimental models of toxoplasmosis.
弓形虫（Toxoplasma gondii）是一种必须存在于细胞内的寄生虫，有三个感染生命阶段--速殖体、缓殖体和孢子虫。组织囊肿破裂后，缓虫重新转化为弓形虫，导致免疫力低下的宿主感染再活化弓形虫病（RT）。本研究的目的是应用 ImageJ 软件分析从一种新建立的 RT 体内模型中获得的刚地弓形虫脑囊肿。用环磷酰胺和氢化可的松治疗慢性感染淋病双球菌（BGD1 和 BGD26 株系）的小鼠（实验组-EG），或作为感染对照组（IC）不进行治疗。小鼠的 RT 通过 qPCR（PCR+）确认；仍处于慢性感染的小鼠为 PCR-。共对 90 张囊肿图像进行了分形维度 (FD)、裂隙度 (L)、直径 (D)、圆度 (C) 和堆积密度 (PD) 分析。与 IC 小鼠相比，PCR+ 小鼠的圆度明显更高（BGD1 小鼠 p < 0.05，BGD26 株小鼠 p < 0.001）。仅在 BGD1 品系的 IC 中观察到 D 和 PD 之间存在明显的负相关（ρ = -0.384，p = 0.048），而分形参数则保持稳定。与攻击性更强的 BGD26 株系相比，BGD1 株系的 D、C 和 PD 明显更高，而裂隙度 L 则更低。总之，这些结果表明了弓形虫囊肿在免疫受损宿主体内结构改变的复杂性，并强调了 ImageJ 在弓形虫病实验模型中的应用潜力。
{"title":"Structural Characterization of Toxoplasma gondii Brain Cysts in a Model of Reactivated Toxoplasmosis Using Computational Image Analysis","authors":"N. Bauman, J. Srbljanović, Ivana Čolović Čalovski, Olivera Lijeskić, V. Ćirković, Jelena Trajković, B. Bobić, Andjelija Ž. Ilić, T. Štajner","doi":"10.3390/fractalfract8030175","DOIUrl":"https://doi.org/10.3390/fractalfract8030175","url":null,"abstract":"Toxoplasma gondii is an obligate intracellular parasite existing in three infectious life stages—tachyzoites, bradyzoites, and sporozoites. Rupture of tissue cysts and re-conversion of bradyzoites to tachyzoites leads to reactivated toxoplasmosis (RT) in an immunocompromised host. The aim of this study was to apply ImageJ software for analysis of T. gondii brain cysts obtained from a newly established in vivo model of RT. Mice chronically infected with T. gondii (BGD1 and BGD26 strains) were treated with cyclophosphamide and hydrocortisone (experimental group—EG) or left untreated as infection controls (ICs). RT in mice was confirmed by qPCR (PCR+); mice remaining chronically infected were PCR−. A total of 90 images of cysts were analyzed for fractal dimension (FD), lacunarity (L), diameter (D), circularity (C), and packing density (PD). Circularity was significantly higher in PCR+ compared to IC mice (p < 0.05 for BGD1, p < 0.001 for the BGD26 strain). A significant negative correlation between D and PD was observed only in IC for the BGD1 strain (ρ = −0.384, p = 0.048), while fractal parameters were stable. Significantly higher D, C, and PD and lower lacunarity, L, were noticed in the BGD1 compared to the more aggressive BGD26 strain. In conclusion, these results demonstrate the complexity of structural alterations of T. gondii cysts in an immunocompromised host and emphasize the application potential of ImageJ in the experimental models of toxoplasmosis.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140231602","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 : 2024-03-18DOI: 10.3390/fractalfract8030174
Shanyuan Qin, Jidong Yang, Ning Qin, Jianping Huang, Kun Tian
In seismic modeling and reverse time migration (RTM), incorporating anisotropy is crucial for accurate wavefield modeling and high-quality images. Due to the trade-off between computational cost and simulation accuracy, the pure quasi-P-wave equation has good accuracy to describe wave propagation in tilted transverse isotropic (TTI) media. However, it involves a fractional pseudo-differential operator that depends on the anisotropy parameters, making it unsuitable for resolution using conventional solvers for fractional operators. To address this issue, we propose a novel pure quasi-P-wave equation with a generalized fractional convolution operator in TTI media. First, we decompose the conventional pure quasi-P-wave equation into an elliptical anisotropy equation and a fractional pseudo-differential correction term. Then, we use a generalized fractional convolution stencil to approximate the spatial-domain pseudo-differential term through the solution of an inverse problem. The proposed approximation method is accurate, and the wavefield modeling method based on it also accurately describes quasi-P-wave propagation in TTI media. Moreover, it only increases the computational cost for calculating mixed partial derivatives compared to those in vertical transverse isotropic (VTI) media. Finally, the proposed wavefield modeling method is utilized in RTM to correct the anisotropic effects in seismic imaging. Numerical RTM experiments demonstrate the flexibility and viability of the proposed method.
在地震建模和反向时间迁移（RTM）中，纳入各向异性对于精确的波场建模和高质量的图像至关重要。由于计算成本和模拟精度之间的权衡，纯准 P 波方程在描述倾斜横向各向同性（TTI）介质中的波传播时具有良好的精度。然而，它涉及一个依赖于各向异性参数的分数伪微分算子，因此不适合使用传统的分数算子求解器进行求解。为了解决这个问题，我们提出了一种在 TTI 介质中带有广义分数卷积算子的新型纯准 P 波方程。首先，我们将传统的纯准 P 波方程分解为椭圆各向异性方程和分数伪差分修正项。然后，我们使用广义分数卷积模板，通过求解逆问题来近似空间域伪差分项。所提出的近似方法是精确的，基于它的波场建模方法也能准确描述准 P 波在 TTI 介质中的传播。此外，与垂直横向各向同性（VTI）介质相比，它只增加了计算混合偏导数的计算成本。最后，建议的波场建模方法可用于 RTM，以校正地震成像中的各向异性效应。RTM 数值实验证明了所提方法的灵活性和可行性。
{"title":"Quasi-P-Wave Reverse Time Migration in TTI Media with a Generalized Fractional Convolution Stencil","authors":"Shanyuan Qin, Jidong Yang, Ning Qin, Jianping Huang, Kun Tian","doi":"10.3390/fractalfract8030174","DOIUrl":"https://doi.org/10.3390/fractalfract8030174","url":null,"abstract":"In seismic modeling and reverse time migration (RTM), incorporating anisotropy is crucial for accurate wavefield modeling and high-quality images. Due to the trade-off between computational cost and simulation accuracy, the pure quasi-P-wave equation has good accuracy to describe wave propagation in tilted transverse isotropic (TTI) media. However, it involves a fractional pseudo-differential operator that depends on the anisotropy parameters, making it unsuitable for resolution using conventional solvers for fractional operators. To address this issue, we propose a novel pure quasi-P-wave equation with a generalized fractional convolution operator in TTI media. First, we decompose the conventional pure quasi-P-wave equation into an elliptical anisotropy equation and a fractional pseudo-differential correction term. Then, we use a generalized fractional convolution stencil to approximate the spatial-domain pseudo-differential term through the solution of an inverse problem. The proposed approximation method is accurate, and the wavefield modeling method based on it also accurately describes quasi-P-wave propagation in TTI media. Moreover, it only increases the computational cost for calculating mixed partial derivatives compared to those in vertical transverse isotropic (VTI) media. Finally, the proposed wavefield modeling method is utilized in RTM to correct the anisotropic effects in seismic imaging. Numerical RTM experiments demonstrate the flexibility and viability of the proposed method.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140231553","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 : 2024-03-16DOI: 10.3390/fractalfract8030173
Mengru Liu, Lihong Zhang
This article mainly studies the double index logarithmic nonlinear fractional g-Laplacian parabolic equations with the Marchaud fractional time derivatives ∂tα. Compared with the classical direct moving plane method, in order to overcome the challenges posed by the double non-locality of space-time and the nonlinearity of the fractional g-Laplacian, we establish the unbounded narrow domain principle, which provides a starting point for the moving plane method. Meanwhile, for the purpose of eliminating the assumptions of boundedness on the solutions, the averaging effects of a non-local operator are established; then, these averaging effects are applied twice to ensure that the plane can be continuously moved toward infinity. Based on the above, the monotonicity of a positive solution for the above fractional g-Laplacian parabolic equations is studied.
{"title":"Monotone Positive Radial Solution of Double Index Logarithm Parabolic Equations","authors":"Mengru Liu, Lihong Zhang","doi":"10.3390/fractalfract8030173","DOIUrl":"https://doi.org/10.3390/fractalfract8030173","url":null,"abstract":"This article mainly studies the double index logarithmic nonlinear fractional g-Laplacian parabolic equations with the Marchaud fractional time derivatives ∂tα. Compared with the classical direct moving plane method, in order to overcome the challenges posed by the double non-locality of space-time and the nonlinearity of the fractional g-Laplacian, we establish the unbounded narrow domain principle, which provides a starting point for the moving plane method. Meanwhile, for the purpose of eliminating the assumptions of boundedness on the solutions, the averaging effects of a non-local operator are established; then, these averaging effects are applied twice to ensure that the plane can be continuously moved toward infinity. Based on the above, the monotonicity of a positive solution for the above fractional g-Laplacian parabolic equations is studied.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140236251","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 : 2024-03-16DOI: 10.3390/fractalfract8030172
Ni Zhang, Wu-Yang Zhu, Peng Jin, Guo Huang, Yi-Fei Pu
With the rise of social media and the internet, the rapid dissemination of information has increased the likelihood of reputation infringement. This study utilizes judicial big data and AI to analyze intrinsic connections in reputation infringement cases, aiding judges in delivering consistent rulings. The challenge lies in balancing freedom of speech with the right to reputation and addressing the ambiguity and subjectivity in infringement cases. This research constructs a structured reputation infringement case dataset from Chinese Judgments Online. It introduces a Fractional Fuzzy Neural System (FFNS) to tackle the vagueness in reputation infringement acts and judicial language, enhancing prediction accuracy for case outcomes. The FFNS, integrating fractional calculus, fuzzy logic, and neural networks, excels in adaptability and nonlinear modeling. It uses fractional order fuzzy membership functions to depict the extent and severity of reputation infringement accurately, combining these outputs with neural networks for predictive analysis. The result is a more precise adjudication tool, demonstrating significant potential for judicial application.
{"title":"Fractional Fuzzy Neural System: Fractional Differential-Based Compensation Prediction for Reputation Infringement Cases","authors":"Ni Zhang, Wu-Yang Zhu, Peng Jin, Guo Huang, Yi-Fei Pu","doi":"10.3390/fractalfract8030172","DOIUrl":"https://doi.org/10.3390/fractalfract8030172","url":null,"abstract":"With the rise of social media and the internet, the rapid dissemination of information has increased the likelihood of reputation infringement. This study utilizes judicial big data and AI to analyze intrinsic connections in reputation infringement cases, aiding judges in delivering consistent rulings. The challenge lies in balancing freedom of speech with the right to reputation and addressing the ambiguity and subjectivity in infringement cases. This research constructs a structured reputation infringement case dataset from Chinese Judgments Online. It introduces a Fractional Fuzzy Neural System (FFNS) to tackle the vagueness in reputation infringement acts and judicial language, enhancing prediction accuracy for case outcomes. The FFNS, integrating fractional calculus, fuzzy logic, and neural networks, excels in adaptability and nonlinear modeling. It uses fractional order fuzzy membership functions to depict the extent and severity of reputation infringement accurately, combining these outputs with neural networks for predictive analysis. The result is a more precise adjudication tool, demonstrating significant potential for judicial application.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140236406","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 : 2024-03-15DOI: 10.3390/fractalfract8030171
Zheng-Xin Wang, Yue-Ting Li, Ling-Fei Gao
The quantile regression technique is introduced into the Lotka–Volterra ecosystem analysis framework. The quantile grey Lotka–Volterra model is established to reveal the dynamic trade relationship between China and the United States. An optimisation model is constructed to solve optimum quantile parameters. The empirical results show that the quantile grey Lotka–Volterra model shows higher fitting accuracy and reveals the trade relationships at different quantiles based on quarterly data on China–US trade from 1999 to 2019. The long-term China–US trade relationship presents a prominent predator–prey relationship because exports from China to the US inhibited China’s imports from the United States. Moreover, we divide samples into five stages according to four key events, China’s accession to the WTO, the 2008 global financial crisis, the weak global economic recovery in 2015, and the 2018 China–US trade war, recognising various characteristics at different stages.
{"title":"Identification of the Dynamic Trade Relationship between China and the United States Using the Quantile Grey Lotka–Volterra Model","authors":"Zheng-Xin Wang, Yue-Ting Li, Ling-Fei Gao","doi":"10.3390/fractalfract8030171","DOIUrl":"https://doi.org/10.3390/fractalfract8030171","url":null,"abstract":"The quantile regression technique is introduced into the Lotka–Volterra ecosystem analysis framework. The quantile grey Lotka–Volterra model is established to reveal the dynamic trade relationship between China and the United States. An optimisation model is constructed to solve optimum quantile parameters. The empirical results show that the quantile grey Lotka–Volterra model shows higher fitting accuracy and reveals the trade relationships at different quantiles based on quarterly data on China–US trade from 1999 to 2019. The long-term China–US trade relationship presents a prominent predator–prey relationship because exports from China to the US inhibited China’s imports from the United States. Moreover, we divide samples into five stages according to four key events, China’s accession to the WTO, the 2008 global financial crisis, the weak global economic recovery in 2015, and the 2018 China–US trade war, recognising various characteristics at different stages.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140238746","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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