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Hermite-Hadamard-Type Inequalities for h -Preinvex Functions via Generalized Fractional Integrals h -预逆函数的hermite - hadamard型不等式
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501677
Xu Wang,Dafang Zhao
{"title":"Hermite-Hadamard-Type Inequalities for\u0000 h\u0000 -Preinvex Functions via Generalized Fractional Integrals","authors":"Xu Wang,Dafang Zhao","doi":"10.1142/s0218348x26501677","DOIUrl":"https://doi.org/10.1142/s0218348x26501677","url":null,"abstract":"Research on fractional-order Hermite-Hadamard (H-H) inequalities has predominantly relied on single convexity assumptions, limiting its adaptability to generalized convexity contexts such as h-preinvex functions. This paper refines the framework of fractional-order H-H inequalities for preinvex functions by leveraging the generalized Riemann-Liouville fractional integral operator. Specifically, a novel class of H-H-type inequalities is constructed and rigorously proved for h-preinvex functions. These results not only generalize and improve classical findings in existing literature but also reveal intrinsic connections between the inequalities. The validity of our conclusions is demonstrated through concrete examples and numerical visualizations, offering new insights for generalized convexity theory and fractional integral inequalities.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Fractal Deep Image Prior with Reliability-Weighted Charbonnier Fidelity for Salt-and-Pepper Image Denoising 基于信度加权Charbonnier保真度的分形深度图像去噪
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501707
Zhihui Tu,Weihang Niu,Jian Lu
{"title":"A Fractal Deep Image Prior with Reliability-Weighted Charbonnier Fidelity for Salt-and-Pepper Image Denoising","authors":"Zhihui Tu,Weihang Niu,Jian Lu","doi":"10.1142/s0218348x26501707","DOIUrl":"https://doi.org/10.1142/s0218348x26501707","url":null,"abstract":"Salt-and-pepper noise (SPN) is a challenging impulsive degradation because a small fraction of severely corrupted pixels can dominate quadratic observation models. However, quadratic data-fidelity terms remain common in unsupervised and hybrid approaches used for SPN removal, despite their sensitivity to sparse extreme residuals. In this paper, we propose RWFracDIP, an unsupervised Fractal Deep Image Prior with Reliability-Weighted Charbonnier Fidelity for SPN removal. RW-FracDIP combines Fractal Image Coding (FIC), Total Variation (TV) regularization, and DIP within a unified formulation, in which the quadratic observation term is replaced by a reliability-weighted Charbonnier fidelity and the reliability map is estimated directly from the noisy image to downweight suspected impulse pixels. The resulting formulation is optimized by an ADMM-style alternating scheme that preserves the complementary roles of fractal self-similarity, TV regularization, and the deep prior. Across five standard grayscale images and four SPN levels, RW-FracDIP achieves the best PSNR in all tested settings and the best SSIM in most of them against DnCNN, DIP, L1/TV, and a FIC+DIP+TV baseline, indicating robustness under impulsive corruption.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energy-Dependent Fractal Fingerprinting of Electron Transport in Gaseous Media 气体介质中电子输运的能量依赖分形指纹图谱
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501689
Ghassan Ragheb,Walid Tarraf,Elie Atieh,Diogo Queiros-Conde,Rafik Absi,Adnan Naja
{"title":"Energy-Dependent Fractal Fingerprinting of Electron Transport in Gaseous Media","authors":"Ghassan Ragheb,Walid Tarraf,Elie Atieh,Diogo Queiros-Conde,Rafik Absi,Adnan Naja","doi":"10.1142/s0218348x26501689","DOIUrl":"https://doi.org/10.1142/s0218348x26501689","url":null,"abstract":"Quantifying how electron trajectory geometry evolves with incident energy across chemically distinct media is central to radiation physics and electron microscopy, yet systematic energy-dependent fractal analysis remains scarce. Here, we report a Monte Carlo investigation of the energy dependence of the fractal dimension D(E) for six gaseous species (He, CH 4 , NH 3 , CO 2 , O 3 , Xe) at uniform density (5 g/cm 3 ) over 25-100-Kev, using the CASINO code combined with box-counting analysis validated against the Koch curve ([Formula: see text], relative error [Formula: see text]%). The parameters of the exponential model [Formula: see text] define species-specific spectral fingerprints. A reversibility efficiency [Formula: see text](E), defined analytically from these parameters, quantifies the degree of geometric complexity of the trajectories as a function of energy and serves as a complementary discriminating descriptor. Our findings suggest potential applications in atmospheric sensing and plasma diagnostics.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fractal Dynamics Exploration and Hybrid Control of a Time-Delayed Fractional-Order Plankton System 时滞分数阶浮游生物系统的分形动力学探索与混合控制
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501690
Yarong Zhang,Cheng Xie,Eerdun Buhe
{"title":"Fractal Dynamics Exploration and Hybrid Control of a Time-Delayed Fractional-Order Plankton System","authors":"Yarong Zhang,Cheng Xie,Eerdun Buhe","doi":"10.1142/s0218348x26501690","DOIUrl":"https://doi.org/10.1142/s0218348x26501690","url":null,"abstract":"The present paper puts forward a time-delayed fractional-order phytoplankton-zooplankton system and systematically investigates its fractal dynamics, stability, bifurcation mechanism, and control strategy. Firstly, the existence, uniqueness, positivity and boundedness of solutions are derived. The equilibrium’s stability is analyzed, and the critical condition for delay-induced Hopf bifurcation is obtained. Subsequently, a nonlinear time-delayed feedback controller is introduced with the objective of suppressing unstable oscillations and bifurcation behaviors. The discussion encompasses the stability and bifurcation of the controlled system, demonstrating the efficacy of the controller in expanding the stable region and constraining fractal-like oscillatory patterns. Finally, the results of the theoretical model are verified by means of numerical simulations. This study contributes to the fractal and fractional dynamics of ecological models and provides a theoretical basis for the stability regulation of plankton systems.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized Nabla Fractional Difference Operators with Discrete Exponential and Mittag-Leffler Kernels 具有离散指数和Mittag-Leffler核的归一化Nabla分数差分算子
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x2650163x
Chafia Laouar,Thabet Abdeljawad,Manar A. Alqudah
{"title":"Normalized Nabla Fractional Difference Operators with Discrete Exponential and Mittag-Leffler Kernels","authors":"Chafia Laouar,Thabet Abdeljawad,Manar A. Alqudah","doi":"10.1142/s0218348x2650163x","DOIUrl":"https://doi.org/10.1142/s0218348x2650163x","url":null,"abstract":"Fractional calculus provides an effective framework for modeling memory effects, but classical discrete fractional operators may exhibit structural inconsistencies at the initial node. In this paper, we introduce normalized nabla Atangana-Baleanu and Caputo-Fabrizio fractional operators together with their associated normalized fractional sums. The proposed normalization preserves the nonlocal memory effects while ensuring well-posedness. We establish generalized nabla Gröwall-type inequalities and comparison principles involving discrete Mittag-Leffler kernels, leading to sufficient conditions for the existence, uniqueness, stability, and boundedness of solutions. Explicit formulations are derived for representative normalized fractional initial value problems, including a discrete recurrence formula and an equivalent continuous Volterra integral equation. Numerical results confirm the theoretical analysis and show that both discrete and continuous solutions approach their respective classical limits as the fractional order increases.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relationship Between the Fractal Dimension and the sum of edge Lin-Lu-Yau Ricci Curvatures on two types of fractal model networks 两类分形模型网络的分形维数与边缘linu - lu - yau Ricci曲率和的关系
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501744
Zhi-Wei Xiong,Zu-Guo Yu,Jian-Hui Li
{"title":"Relationship Between the Fractal Dimension and the sum of edge Lin-Lu-Yau Ricci Curvatures on two types of fractal model networks","authors":"Zhi-Wei Xiong,Zu-Guo Yu,Jian-Hui Li","doi":"10.1142/s0218348x26501744","DOIUrl":"https://doi.org/10.1142/s0218348x26501744","url":null,"abstract":"We aim to study the relationship between the fractal dimension and the Lin-Lu-Yau Ricci curvature in complex networks in this paper. We analyzed two types of networks with fractal properties, and compared the total edge Lin-Lu-Yau Ricci curvature with the fractal dimension of the complex networks from a global point of view. Except for a special case of one type of fractal network (i.e., a tree graph), we observed a quantitative relationship with the diameter of the network, thereby linking two important properties of complex networks. We found that the sum of the Lin-Lu-Yau Ricci curvatures of tree graphs is constantly 2. These properties provide a new perspective for analyzing complex networks and help us better understand their characteristics.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"168 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variable-Order Riemann-Liouville Integrals on the Box Dimension of Graphs of Continuous Functions 连续函数图的盒维上的变阶Riemann-Liouville积分
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501720
Yeyu Peng,Kui Yao,Xia Zhang,Nan Li,Zhe Wang
{"title":"Variable-Order Riemann-Liouville Integrals on the Box Dimension of Graphs of Continuous Functions","authors":"Yeyu Peng,Kui Yao,Xia Zhang,Nan Li,Zhe Wang","doi":"10.1142/s0218348x26501720","DOIUrl":"https://doi.org/10.1142/s0218348x26501720","url":null,"abstract":"This paper investigates the effect of the variable-order Riemann-Liouville fractional integral operator on the box dimension of graphs of continuous functions. By constructing a counterexample, we show that even when the integrand is a constant function, the graph of the resulting integral has box dimension strictly greater than 1 if the order function exhibits fractal characteristics, revealing an essential difference between variable-order and constant-order fractional operators. On the other hand, we provide a sufficient condition ensuring that the output graph has box dimension equal to 1: if the order function is Lipschitz continuous with a positive lower bound and the integrand satisfies an appropriate H¨older continuity condition, then the resulting integral belongs to the class of absolutely continuous functions, and hence its graph has box dimension 1. Numerical simulations illustrate the conclusion of the counterexample.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hermite-Hadamard Type Inequalities for Multiplicative Fractional Integrals of Log-Harmonically h -Convex Functions 对数调和h -凸函数的分数阶乘法积分的Hermite-Hadamard型不等式
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501616
Huiyun Zeng,Xuexiao You,Dafang Zhao
{"title":"Hermite-Hadamard Type Inequalities for Multiplicative Fractional Integrals of Log-Harmonically\u0000 h\u0000 -Convex Functions","authors":"Huiyun Zeng,Xuexiao You,Dafang Zhao","doi":"10.1142/s0218348x26501616","DOIUrl":"https://doi.org/10.1142/s0218348x26501616","url":null,"abstract":"This paper develops and extends Hermite-Hadamard type inequalities for log-harmonically [Formula: see text]-convex functions using multiplicative Riemann-Liouville fractional integrals within the context of multiplicative calculus. In particular, we establish new inequalities for the products and quotients of log-harmonically [Formula: see text]-convex functions. Furthermore, new inequalities involving multiplicative Riemann-Liouville fractional integrals are developed for combinations of log-harmonically [Formula: see text]-convex and harmonically convex functions, including their products and quotients. Numerical examples and graphical illustrations confirm the validity and practical relevance of the results.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"456 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical Lemon Disease Model via Fractal-Fractional Operators: Analysis Under the Caputo Formulation with Numerical Comparison to Atangana-Baleanu-Caputo and Caputo-Fabrizio 基于分形-分数算子的柠檬病数学模型：Caputo公式下的分析及与Atangana-Baleanu-Caputo和Caputo- fabrizio的数值比较
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501665
Gunaseelan Mani,Subramanian Chinnachamy,Kannan Muniasamy,Sabri T. M. Thabet,Thabet Abdeljawad,Taoufik Moulahi
{"title":"Mathematical Lemon Disease Model via Fractal-Fractional Operators: Analysis Under the Caputo Formulation with Numerical Comparison to Atangana-Baleanu-Caputo and Caputo-Fabrizio","authors":"Gunaseelan Mani,Subramanian Chinnachamy,Kannan Muniasamy,Sabri T. M. Thabet,Thabet Abdeljawad,Taoufik Moulahi","doi":"10.1142/s0218348x26501665","DOIUrl":"https://doi.org/10.1142/s0218348x26501665","url":null,"abstract":"Citrus diseases impose substantial annual losses on global agriculture, threatening both food supply and the economic returns of growers worldwide. In this study, we advance the mathematical understanding of multi-pathogen citrus disease dynamics using fractal-fractional calculus in the Caputo sense. We examine the equilibrium points of the proposed model and establish the existence, uniqueness, and Hyers-Ulam stability of its solutions under the fractal-fractional Caputo (FF Caputo) formulation. We further formulate a numerical scheme based on the generalized Euler method and implement it under three related fractal-fractional operators (FF Caputo, Atangana-Baleanu-Caputo, and Caputo-Fabrizio) to compare their predicted disease dynamics under a range of parameter scenarios. The resulting simulations provide insight into disease progression and inform the design of disease-management strategies. By providing a mathematical basis for the control of plant disease, this work contributes to Sustainable Development Goals 2 (Zero Hunger) and 3 (Good Health and Well-being), supporting sustainable agriculture, plant health, and food security.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical study of heat transfer by Rayleigh-Benard convection in variable viscosity Newtonian liquids: A weak non-linear theory 变粘度牛顿流体中瑞利-贝纳德对流换热的解析研究：一个弱非线性理论
Fractals Pub Date : 2026-10-15 DOI: 10.1142/s0218348x26501628
A. S. Aruna,M. Girinath Reddy,N. Kavitha,Iskander Tlili
{"title":"Analytical study of heat transfer by Rayleigh-Benard convection in variable viscosity Newtonian liquids: A weak non-linear theory","authors":"A. S. Aruna,M. Girinath Reddy,N. Kavitha,Iskander Tlili","doi":"10.1142/s0218348x26501628","DOIUrl":"https://doi.org/10.1142/s0218348x26501628","url":null,"abstract":"Chaotic convection finds extensive application across diverse physical and mechanical phenomena, weather prediction, crystal production, satellite motion within our solar system, and ecological dynamics. Its widespread utility underscores its significance in understanding and analyzing complex systems in numerous fields. The study deals with the dynamics of regular and chaotic convection within a Newtonian fluid with variable viscosity confined between two infinitely extended horizontal layers with temperature gradient (Rayleigh-Benard convection problem). Employing the Galerkin technique and using minimal representation of Fourier series, a three-dimensional generalized Lorenz nonlinear model is derived. The generalized Lorenz model derived is numerically solved and phase portraits are utilized to analyze the system’s qualitative dynamics. The onset of chaos in conventional fluid configurations occurs at a scaled Rayleigh number [Formula: see text] of 24.7368. Additionally, a weakly nonlinear analysis is performed to comprehend the heat transport within the fluid layer concerning the variation of the scaled Rayleigh number and thermorheological parameter. It is demonstrated that the onset of convection occurs at significantly lower Rayleigh numbers in fluids with exponentially decreasing viscosity compared with fluids of constant viscosity. Furthermore, an increase in the thermorheological parameter leads to an earlier transition from regular to chaotic convection.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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