Fractals最新文献

{"title":"A Comprehensive Study of Fractal Models for Permeabilities under Thermo-Hydro-Mechanical Interactions and Slip Effect in Porous Coal Rocks","authors":"Ningyuan Guo,Tian Xia,Qiang Li,Xianyang Zou,Guannan Liu,Guangsheng Zhu,Boming Yu","doi":"10.1142/s0218348x26501653","DOIUrl":"https://doi.org/10.1142/s0218348x26501653","url":null,"abstract":"The complex pore-fracture dual-medium structure in coal reservoirs plays an important role during methane extraction. However, it remains a challenge to elucidate the effects of fracture aperture variation and gas slip on gas transport under thermo-hydro-mechanical (THM) interactions. In this paper, fractal geometry theory was applied to characterize the microstructures of porous coal rocks, and this work developed a three-dimensional (3D) THM coupling model that incorporates fractureaperture variation and the slip effect. This model enables simultaneous analysis of the stress field, porosity, permeability, seepage field, and temperature field. Furthermore, we analyzed the evolution of the slip effect with microstructural parameters, including: (1) fractal dimensionfor tortuosity; (2) fracture roughness; and (3) fluctuation amplitude of fracture cross-section size. The effects of Langmuir adsorption parameters on continuous and slip flow permeabilities were also calculated. The present results indicate that the slip effect enhances permeability in both pore and fracture systems, with a more prominent influence on pores. The fractal dimension for tortuosity exerts the strongest inhibitory effect on slip-flow permeability, followed by the fluctuation amplitude of fracture cross-section size, while fracture roughness has the weakest influence. The Langmuir adsorption parameters exhibit differentiated properties of continuous and slip flow.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210379","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":"New Hermite-Hadamard Type Integral Inequalities for Generalized Preinvex Functions via Yang Local Fractional Calculus","authors":"Jose E. Sanabria,Rainier V. Sanchez C,Xiao-Jun Yang","doi":"10.1142/s0218348x26501719","DOIUrl":"https://doi.org/10.1142/s0218348x26501719","url":null,"abstract":"In this manuscript, we establish new local fractional integral inequalities of Hermite-Hadamard type for generalized preinvex functions in the fractal field [Formula: see text], where [Formula: see text] denotes the fractal dimension. The main results are obtained via a new local fractional integral identity involving the invex trajectories [Formula: see text] and [Formula: see text]. By combining this identity with generalized preinvexity, the generalized Hölder inequality, and a generalized power-mean integral inequality, we obtain several estimates for functions whose local fractional derivatives, as well as powers of their absolute values, are generalized preinvex. A distinctive feature of our approach is that the proofs do not require the classical Condition [Formula: see text] typically imposed on the bifunction [Formula: see text] in related literature. We discuss several particular cases, showing that known inequalities for generalized convex functions are recovered when [Formula: see text]. Finally, as applications, we obtain estimates involving generalized probability density functions, cumulative distribution functions, and expected values within the framework of Yang’s local fractional calculus.","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":"149208882","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 Gauss-Lobatto error bounds for multiplicatively twice-differentiable functions via multiplicative (mu,Mu)-Riemann-Liouville Integrals","authors":"Xiaoyan Qiu,Tingsong Du","doi":"10.1142/s0218348x26501732","DOIUrl":"https://doi.org/10.1142/s0218348x26501732","url":null,"abstract":"This paper initiates the study by establishing Gauss-Lobatto-type identity for multiplicatively twice-differentiable [Formula: see text]-convex functions within the framework of multiplicative [Formula: see text]-Riemann-Liouville fractional integrals. Subsequently, we develop Gauss-Lobatto-type inequalities under the following two conditions: (i) [Formula: see text] is multiplicatively [Formula: see text]-convex, or (ii) [Formula: see text] is [Formula: see text]-convex [Formula: see text]. To substantiate the theoretical findings, we further provide numerical simulations and graphical representations that elucidate the practical implications of our analysis. Lastly, we highlight the utility of the established inequalities in the context of quadrature formulas and special means.","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":"149208885","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":"Analytical Investigation of Time-Fractional Black-Scholes Equations with Caputo Derivatives using the Yang Perturbation Transform Method","authors":"Jinxing Liu,Jingmei Peng,Huailing Luo,Huaping Xiao","doi":"10.1142/s0218348x26501641","DOIUrl":"https://doi.org/10.1142/s0218348x26501641","url":null,"abstract":"The Black-Scholes model plays a significant role in the analysis of financial derivatives and option pricing. However, the classical framework may not fully capture the memory and hereditary effects observed in financial markets. This study investigates a time-fractional Black-Scholes equation involving the Caputo fractional derivative and develops a semi-analytical approach for its solution. The proposed scheme transforms the governing fractional differential equation into a recursive algebraic formulation without requiring temporal or spatial discretization, linearization, or restrictive assumptions. The effectiveness of the proposed approach is demonstrated through several illustrative examples, and the resulting solutions are compared with the corresponding classical solutions. Furthermore, the numerical results and graphical analyses demonstrate the accuracy and effciency of the proposed method, while the rapid convergence of the resulting series confirms its consistency and computational effectiveness.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208904","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-Memory Deformation of an Apsidal Precession Resonance: Finite-Time Trapping and Trapped-Interval Diagnostics","authors":"Mohamed R. Amin","doi":"10.1142/s0218348x27400251","DOIUrl":"https://doi.org/10.1142/s0218348x27400251","url":null,"abstract":"A fractional-memory deformation of a reduced apsidal precession resonance model is developed as a controlled phenomenological extension of an established Hamiltonian resonant backbone. The conservative reference system is taken to be a one-degree-of-freedom Hamiltonian apsidal resonance with a positive-action resonance crossing, a libration center, a saddle point, a separatrix, and a finite classical resonance width. Fractional memory is therefore not introduced to generate the resonance, but to deform an existing resonant structure. The ordinary secular equations are replaced by Caputo fractional equations, yielding a history-dependent extension of the conservative reduced model rather than a first-principles derivation of astrophysical memory. The integer-order limit is used as a validation case, while fractional orders below unity are used to examine memory-modified dynamics. Numerical integrations are performed using a fractional Adams-Bashforth-Moulton predictor-corrector scheme. Finite-time diagnostics are introduced to measure libration-envelope deformation, projected phase-space changes, finite-time trapped-interval response, separatrix-region ambiguity, clean versus marginal behavior, and trapping-time transitions. The conservative Hamiltonian resonance is accurately recovered in the integer-order limit. For fractional orders below unity, the resonant backbone is found to remain visible in the clean regime, while the observable libration envelope is deformed and the projected phase-space curves no longer behave as closed Hamiltonian level sets. Near the classical separatrix, delayed escape and ambiguous finite-time trapping are observed, indicating increased separatrix-region ambiguity under the adopted diagnostic protocol. In the marginal near-boundary regime, the measured finite-time trapped set can approach the singular action boundary, making the measured trapped interval boundary-sensitive rather than an invariant Hamiltonian resonance width. These results provide a reduced fractional-dynamical framework for studying memory-deformed resonant trapping, while mechanism-specific astrophysical memory kernels remain a subject for future work.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208913","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":"Discretization, Transformation and Analysis of the COVID-19 Wave Epidemic with Fractal Fractional Operator","authors":"Kottakkaran Sooppy Nisar,Muhammad Farman","doi":"10.1142/s0218348x26400761","DOIUrl":"https://doi.org/10.1142/s0218348x26400761","url":null,"abstract":"Currently, it’s far widely recognized reality that fractional evaluation is an enticing area of study, particularly in modeling. This paper discusses the proposed fractional derivatives for the dynamical transmission of the Coronavirus model with the Mittag-Leffler kernel. These are the latest techniques that give useful results in analyzing and controlling COVID-19 infection in the community. Moreover, several strategies, such as fixed-point theory, linear growth, and Ulam-Hyres stability of the suggested operator, have been applied to the fractional order model. To see the effects of the model, we employ the Sumudu transform and an effective method as well. The PID and Controllability of the model is also discussed. Lastly, by creating a computational framework that integrates the stochastic technique of artificial neural networks with Levenberg-Marquardt backpropagation (ANNLMB), we provide the numerical calculations of the suggested model in four distinct variations. The model’s tools are powerful and capable of modelling theoretical conditions. They are also suggested for application in other physical models of infectious diseases.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208906","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":"Multiscale Dynamics of a Tri-Trophic Predator-Prey System with Neural Network Validation","authors":"Aatif Ali,Shahid Khan,Seda Igret Araz,Niaz Ali Shah,Maria Altaib Badawi,Saharuddin Bin Mohamad","doi":"10.1142/s0218348x27400263","DOIUrl":"https://doi.org/10.1142/s0218348x27400263","url":null,"abstract":"A nonlinear three-species predator-prey model containing populations of prey, intermediate predators, and top predators was proposed and examined. To represent more realistic prey growth and saturation mechanisms inherent in ecological systems, the model incorporates exponential functional responses and restricted prey growth. The model’s qualitative dynamics are examined using equilibrium and local stability analysis, and the population time evolution is numerically examined using the Forward Euler and fourth-order Runge-Kutta (RK4) method. Numerical simulations are used to examine the coexistence behavior, oscillatory dynamics, and asymptotic stability over a long enough period of time. After all, the system tends to a stable coexistence equilibrium since the time-series profiles and phase pictures show that the overall population is positive and bounded under suitable parameter values. The numerical results further demonstrate that the nonlinear trophic interactions between the species cause the species to naturally display transitory oscillations. Furthermore, the results show that the RK4 schemes are more numerically stable than the Euler scheme, especially for larger simulation time steps and smaller error tolerances. Analyzes of parameter sensitivity are also carried out in relation to the intrinsic prey growth rate. The findings demonstrate that, although the species continue to coexist over time, oscillatory behavior is stronger and population fluctuations are larger when the prey growth parameter is higher. The incorporation of restricted prey growth with exponential predator response in a tri-trophic ecological framework and a thorough comparison of traditional numerical techniques for stability and convergence analysis are the innovative aspects of this work. The suggested model advances the mathematical understanding of multispecies population dynamics and provides insightful information on the nonlinear interactions among ecological processes. Furthermore, an artificial neural network (ANN) is used to assess the numerical solutions of the model and learn the numerical adjustment between the RK4 and Euler approximations. The ANN accurately replicates the RK4 time-series and phase-space trajectories, achieving one-step prediction errors of order 10 -7 .","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208905","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":"Accelerating the Linearized Quadrature Method for Nonlinear Diffusion Using a Neural Network Surrogate","authors":"Mohammad Akram,Israr Ahmad,Sadique Ahmad,Ala Saleh Alluhaidan,Mohammed A. ElAffendi","doi":"10.1142/s0218348x27400196","DOIUrl":"https://doi.org/10.1142/s0218348x27400196","url":null,"abstract":"In this paper, we investigate the [Formula: see text]-dimensional non-linear porous medium equation under the [Formula: see text]-Hilfer derivative. A comprehensive qualitative analysis of the solution is presented, including existence, uniqueness, and Ulam-Hyers (UH) stability. Moreover, for the numerical simulations, a linearized quadrature method (LQM) is developed for the proposed model. MATLAB numerical simulations comprise two- and three-dimensional plots, which demonstrate how changes in the fractional order [Formula: see text] and type parameter [Formula: see text] influence the dynamics of the solutions. The neural network approach demonstrates excellent predictive capability, accurately capturing the behaviour of the model with high precision. This work advances both the theory and computation of the high-dimensional porous medium flows under the [Formula: see text]-Hilfer derivative.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208912","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":"Zoonotic Disease Transmission Between Baboons and Humans in Al-Baha: A Caputo-Fabrizio Fractal-Fractional Order Modeling Study","authors":"Mohammed Althubyani,Ghanem Al-Ghamdi,Sayed Saber","doi":"10.1142/s0218348x26400773","DOIUrl":"https://doi.org/10.1142/s0218348x26400773","url":null,"abstract":"Baboons in Saudi Arabia’s Al Baha province frequently interact with people, creating crossspecies transmission settings that classical, integer-order epidemic models cannot reproduce. By utilizing the Caputo-Fabrizio fractional operator, we are able to encode history effects via a nonsingular kernel over two hosts with nonlocal memory. Memory strength determines outbreak magnitude, decay rates, and oscillatory patterns across a range of fractional indices. It can precipitate a variety of complex and chaotic transients absent from the integer-order limit. Mathematically, we establish Ulam-Hyers stability for the proposed dynamic, ensuring solution robustness under small perturbations and modelling noise. The resulting methodology offers a principled tool for designing public-health actions and wildlife management policies in regions with sustained human-wildlife interfaces.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208914","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":"COMPREHENSIVE ANALYSIS OF INNOVATIVE FRACTAL-FRACTIONAL DIFFERENTIAL OPERATORS UTILIZING THE GENERALIZED MITTAG-LEFFLER FUNCTION FOR KINETIC SYSTEMS: APPLICATION TO THE LANGMUIR–HINSHELWOOD REACTION MODEL","authors":"FAISAL SULTAN,AIMAN NISAR,ISMAIL NACI CANGUL,MUHAMMAD SOHAIL,YASSER ELMASRY,SALAH KNANI,GILBERT CHAMBASHI,IBRAHIM MAHARIQ","doi":"10.1142/s0218348x25402807","DOIUrl":"https://doi.org/10.1142/s0218348x25402807","url":null,"abstract":"The primary objective of this study is to develop novel difference operators by incorporating the generalized Mittag-Leffler function with fractal derivatives within the framework of kinetic equations. The operators referred to as the Fractal-Fractional Differential Operator and Fractal–Fractional Integral Operator are used to apply to new mathematical fractional models. The primary role is to deal with non-local phenomena in the world and this shows fractal as well as dynamical characteristics. This study investigates the novel properties of these operators, numerical approximation methods for the computation of these operators and their applications in solving different practical problems in real life. The purpose of the research is to improve approaches to bring methods to bear on complex systems with fractal and fractional characteristics. The accuracy of the operators in solving the differential equation systems that were obtained from the kinetic models is shown in the graphical and numerical results and they are found to be excellent.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149090370","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}