Fractals最新文献

{"title":"Fractal control of Julia sets generated by discrete fractional competitive model","authors":"Manoj Kumar,Syed Abbas,Michal Niezabitowski,Marko Kostic","doi":"10.1142/s0218348x26501471","DOIUrl":"https://doi.org/10.1142/s0218348x26501471","url":null,"abstract":"This article explores the fractal behavior of a general non-linear discrete fractionalorder competitive model. In particular, we focus on a discrete fractional competitive model that illustrates the growth of two competing species influenced by toxic compounds. The analysis in this paper can be extended to other discrete fractional competitive models. To date, such models influenced by toxic compounds have not been studied from a fractal perspective, nor has the innovative control method been applied to the control of Julia sets in discrete models. Initially, we presented the discrete fractional competitive model utilizing the Gr¨unwald-Letnikov operator. Following that, we introduced the Julia set produced by a discrete fractional competitive model with the help of a modified escape-time algorithm suitable for the fractional order scenario. The fractal dynamic characteristics and the influence of memory parameters on the Julia set are illustrated through graphical exploration and fractal dimension analysis. Controlling Julia sets of the discrete fractional map is achieved by stabilizing the equilibrium point. The stability of these equilibrium points and consequently, the Julia sets are controlled using two distinct control methods. As the control parameter values diminish in the gradient control method, the Julia set related to the controlled system begins to shrink. This effect is a result of the instability of the equilibrium point. We developed a control scheme that helps in the control of the Julia set. When the control parameter values increase within a specific range, the Julia set in the second new state control technique compresses both vertically and horizontally. Again, this is attributed to the instability of the equilibrium point. To synchronize the Julia sets of two similar systems with different system parameters, a new synchronous controller featuring an arbitrary constant has been developed. The effectiveness of this synchronous controller is evaluated using numerical simulations. Our methodologies and various theoretical studies are solidified with the help of numerical simulations. This analysis will also apply to analogous types of mathematical models with different dimensions.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894805","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}

{"title":"Triple Positive Solutions and Nonexistence Results for Mixed Fractional Differential Equations with p-Laplacian Operator","authors":"Hamza Tabti,Abdelkader Benali,Ibrahim Alraddadi","doi":"10.1142/s0218348x26501410","DOIUrl":"https://doi.org/10.1142/s0218348x26501410","url":null,"abstract":"In this paper, we investigate the existence of multiple positive solutions for a class of nonlinear fractional boundary value problems involving mixed fractional derivatives with a p-Laplacian operator. The analysis is carried out by combining Green’s function techniques with a generalized Avery-Henderson fixed point theorem in cones, which enables us to establish the existence of at least three positive solutions for the considered problem. Moreover, we derive eigenvalue-type conditions under which the associated problem admits no positive solutions. Finally, the theoretical results are illustrated and validated through several representative examples, clarifying the applicability of the obtained theoretical results.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894746","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}

{"title":"Non-Perturbative Analysis of Primary Resonance and Chaos in Fractal Mems Photoacoustic Transducers","authors":"Guang-Qing Feng,Chun-Hui He","doi":"10.1142/s0218348x26501483","DOIUrl":"https://doi.org/10.1142/s0218348x26501483","url":null,"abstract":"The present study proposes a cohesive analytical framework for the primary resonance and chaotic dynamics of fractal-structured MEMS photoacoustic transducers. The non-perturbative approach is extended to fractal MEMS systems, yielding closed-form equivalent linearisation that accurately captures amplitude-dependent behaviour with relative errors below 5%. The analysis demonstrates that fractal parameters significantly regulate dynamic stability. An increase in fractal dimension or a decrease in scale factor has been shown to enhance electrostatic softening, reduce effective nonlinearity, and lower the chaotic threshold through a period-doubling cascade. A fundamental trade-off is evident between sensitivity and stability. The fractal geometries that optimise photoacoustic performance are precisely those that compromise dynamic reliability. The establishment of a design criterion is imperative for ensuring stable operation within the hardening regime. The framework also offers pathways towards fractional-order damping and digital twin integration, providing both theoretical foundations and practical guidelines for robust fractal MEMS design.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894787","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}

{"title":"Assessing the Impact of Quarantine Behavior Among Individuals Infected with Mpox: A Fractional Artificial Neural Network Approach","authors":"Muhammad Farman,Muhammad Asad Ullah,Yuyang Cai,Yang Ling,Usama Ghafoor,Mustafa Bayram,Mohamed Hafez","doi":"10.1142/s0218348x26501501","DOIUrl":"https://doi.org/10.1142/s0218348x26501501","url":null,"abstract":"This study proposed a combination of compartmental modeling with a bio-inspired machine learning (ML) framework for the dynamical analysis of monkeypox (MPOX) transmission. A Caputo fractional-order model is developed based on human infection data from the USA to understand the long-term fluctuation in disease propagation and inherent memory effects. The transmission dynamics of MPOX incorporating vaccination, quarantine, recovery, loss of immunity, and both human to human and animal to human transmission pathways are considered. The fractional-order model is numerically solved using the Adams-Bashforth-Moulton (ABM) method to investigate the effects of fractional order on disease dynamics. Global sensitivity analysis based on Latin hypercube sampling and partial rank correlation coefficient (LHS-PRCC) analysis identifies the key parameters influencing the human reproduction number (R2). To provide an efficient surrogate for the numerical solutions, an artificial neural network (ANN) based on the Levenberg-Marquardt backpropagation (LMB) algorithm is developed. The dataset obtained through ABM is used to reduce the mean square error (MSE) with the statistics of 70% as training and 15% for both testing and validation. The results indicate that human to human transmission is a major driver of the epidemic, whereas timely quarantine and vaccination substantially reduce transmission. The fractional-order formulation further shows that decreasing the fractional order slows epidemic progression and delays the infection peak, highlighting the influence of memory effects on disease dynamics. The proposed fractional-order and neural network framework provides an efficient and reliable approach for eradicating the infectious diseases transmission within the population and for assessing the effectiveness of key intervention strategies.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894786","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}

{"title":"Generalized\u0000 p\u0000 -Convex Inequalities on Fractal Sets with Neural Network Modeling","authors":"Saad Ihsan Butt,Muhammad Mehtab,Mohammed Alammar,Youngsoo Seol","doi":"10.1142/s0218348x26501409","DOIUrl":"https://doi.org/10.1142/s0218348x26501409","url":null,"abstract":"In this article, we developed a new variant of discrete Jensen-type inequality for p-convex functions over fractal sets. Improvement and generalization of some Jensen-Mercer-type estimates for [Formula: see text]-convex function in the framework of fractal fractional calculus are obtained. Using this Jensen-Mercer inequality, we establish a Hermite-Hadamard-Mercer (HHM) type inequalities for [Formula: see text]-convex functions in fractal dimensions. We drive a new integral identity and HHM type inequalities for differentiable [Formula: see text]-convex functions. Some of the results presented here for [Formula: see text]-convex functions are extensions of earlier results for harmonically convex and convex functions. Finally, we also provide a neural network-based numerical analysis of the obtained results, showing the accuracy and effectiveness of the proposed inequalities for [Formula: see text]-convex functions.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894792","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}

{"title":"Fractal Classification of the Environmental Protection Area of\u0000 Pedra do Cavalo","authors":"Basilio Fernandez Fernandez,Lidiane Alves De Oliveira,G. F. Zebende","doi":"10.1142/s0218348x26501434","DOIUrl":"https://doi.org/10.1142/s0218348x26501434","url":null,"abstract":"We perform a spatio-temporal remote sensing analysis at the location of an environmental protection area whose water resources from a lake supply a large part of the metropolitan areas of Salvador and Feira de Santana (the two largest cities in the state of Bahia, Brazil), where about 4,000,000 people live. In this analysis, the pixels of the different images are counted over time, considering five different landscape classes (from MapBiomas). First, descriptive statistics of the area are obtained for the whole territory, which immediately shows that the values vary greatly, due to the change of the classes over time. Thus, if we look at the five classes and count the pixels, it is possible to measure the area-weighted by each class (which was done here). Since counting the pixels of the images for different sizes yielded a power-law, it was possible to calculate the fractal dimension for these images in all classes as a function of time, enabling a correct comparison between the classes by their fractal dimension.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894789","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}

{"title":"FRACTIONAL-ORDER MATHEMATICAL MODELING OF HUMAN PAPILLOMA VIRUS (HPV) USING ARTIFICIAL DEEP NEURAL NETWORKS","authors":"SADIQUE AHMAD,EIMAN,ALTAF KHAN,ALA SALEH ALLUHAIDAN,MOHAMMED A. ELAFFENDI","doi":"10.1142/s0218348x27400111","DOIUrl":"https://doi.org/10.1142/s0218348x27400111","url":null,"abstract":"The study proposes a mathematical framework to evaluate the human papilloma virus (HPV) infection transmission dynamics, taking into account advanced approaches related to fractional calculus. The HPV infection and cervical cancer are always major public health threats across the world, particularly in those areas which have insufficient availability to health care services and control interventions. In first step, the positivity and boundedness of solutions are precisely examined to show that the model remains biologically valuable in the long run. In this study the disease-free equilibrium and endemic equilibrium is provided to describe the long-term behavior of the disease in a population. The basic reproductive number and sensitivity analysis are also studied as these are vital to analyze behavior of the dynamics. The theoretical results are established for the model under consideration using the fixed point theory. Next, the condition for Hyers–Ulam’s (H–U)-type stability is clearly demonstrated. Then, modified Euler’s method (MEM) is applied for the computation of numerical solution of the proposed model. At the end, we give graphical representation of the involved results. We use some real values for the parameters involved in our considered model. MATLAB is used for graphical demonstration. Through a comprehensive numerical analysis, the model explores how various fractional order values influence the dynamics of HPV transmission. Hence, suggestions are provided for how fractional order may better convey the intricate relationships within the communities. These developments also draw awareness to the method’s significance in advancing disease modeling and deepening our knowledge of HPV transmission. With the help of artificial deep neural networks (DNNs), we investigate the considered model. We deduce some statistical thresholds including mean squared error (MSE) and root mean squared error (RMSE) together with progressional analysis. Further, graphical illustrations are given for infected classes using different fractional orders. Absolute errors between the simulated and those predicted by DNNs are compared for various fractional orders.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"163 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894796","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}

{"title":"MULTIPLICATIVE FRACTIONAL MILNE–MERCER-TYPE INEQUALITIES VIA MULTIPLICATIVE PROPORTIONAL CAPUTO–HYBRID–CONFORMABLE INTEGRAL OPERATORS","authors":"JEN CHIEH LO","doi":"10.1142/s0218348x26501367","DOIUrl":"https://doi.org/10.1142/s0218348x26501367","url":null,"abstract":"This paper establishes new Milne–Mercer-type inequalities in the framework of multiplicative fractional calculus. A multiplicative proportional Caputo–Hybrid–Conformable fractional integral operator is introduced, and a corresponding integral identity is derived for multiplicatively differentiable functions. By using multiplicative convexity and logarithmic transformation techniques, several Milne–Mercer-type inequalities are obtained. The proposed results extend classical Milne-type inequalities and include some existing multiplicative fractional inequalities as special cases. Numerical examples and three-dimensional visualizations are also provided to verify the validity of the main inequality and to illustrate the influence of the fractional parameters.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894820","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}

{"title":"THE LIPSCHITZIAN FRACTIONAL DERIVATIVE: USING THE LIPSCHITZ EXPONENT TO UNIFY SPATIAL IRREGULARITY AND TEMPORAL MEMORY","authors":"YHOSVANY SOLER-CASTILLO,J. F. GÓMEZ-AGUILAR,C. JUNG,J. A. HERNÁNDEZ","doi":"10.1142/s0218348x26501318","DOIUrl":"https://doi.org/10.1142/s0218348x26501318","url":null,"abstract":"The study proposes a new fractional operator termed the Lipschitzian Fractional Derivative (LFD) that directly links the differentiation order to the Lipschitz Exponent (LE) of functions. This means that instead of enforcing a fixed fractional order, the operator adjusts to the function’s actual smoothness or irregularity. The derivative naturally connects fractional calculus (order-based) and fractal calculus (dimension-based), since the LE can be understood as a measure of local fractal dimension. It is therefore a bridge operator. It unifies spatial irregularity (fractal dimension) and temporal smoothness (fractional order). This implies that memory effects and fractal geometry can be described simultaneously by a single operator. The Atangana operators provide a natural generalization of the Marchaud derivative in fractal contexts. They allow modeling of systems where both temporal memory and spatial fractality overlap, for example, diffusion in porous media, or anomalous transport in astrophysical systems. A natural way to combine smoothness-based fractional operators with dimension-based fractal operators is to tie the differentiation order directly to the LE. In this manner, the operator uses only one parameter rather than the two of Atangana’s operators to encode both the regularity of the function and the fractality of the geometry. This could lead to a common framework for researching singularities, anomalous diffusion, and fractal dynamics in applied mathematics, physics, and engineering.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894489","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}

{"title":"TECHNICAL NOTE — UNVEILING SOLITON DYNAMICS IN NONLINEAR SPATIOTEMPORAL FRACTIONAL QUANTUM MECHANICS EQUATION: AN ANALYTICAL EXPLORATION USING AN INNOVATIVE TECHNIQUE","authors":"MUHAMMAD BILAL,JAVED IQBAL,IKRAM ULLAH,ALHANOUF ALBURAIKAN,SALAH BOULAARAS,HAMIDEN ABD EL-WAHED KHALIFA,Juan E. Nápoles Valdes","doi":"10.1142/s0218348x26710015","DOIUrl":"https://doi.org/10.1142/s0218348x26710015","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894490","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}