A model of a layered hierarchically constructed composite is presented, the structure of which demonstrates the properties of similarity at different scales. For the proposed model of the composite, fractal analysis was carried out, including an asse...
Compartment modeling is a widely accepted technique in the field of pharmacokinetic analysis. However, conventional compartment modeling is performed under a homogeneity assumption that is not a naturally occurring condition. Since the assumption lac...
To study the peculiarities of anomalous consolidation processes in saturated porous (soil) media in the conditions of salt transfer, we present a new mathematical model developed on the base of the fractional-fractal approach that allows considering...
In this study, we propose a dynamic fractal dimension modeling (DFDM) framework that integrates image analysis, wavelet-based fractal methods, and structural fractal geometry to quantify the evolution of pore complexity. Unlike conventional static fr...
This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension
Breast cancer ranks among the most prevalent malignancies affecting the female population and is a prominent contributor to cancer-related mortality. Mathematical modeling is a significant tool that can be employed to comprehend the dynamics of breas...
Conventional high-pressure mercury injection (HPMI) alone inadequately characterizes the fractal properties of nanopores in tight sandstone reservoirs, and existing fractal models for HPMI, low-temperature nitrogen adsorption (LTNA), and nuclear magn...
To address the data management limitations of traditional ontology models in dynamic industrial settings, this study introduces the Fractal Fuzzy Ontology Modeling (FFOM) framework, a novel methodology for optimizing data management, integration, and...
The closed mesoporous polymer gels have garnered significant attention as advanced thermal insulation materials due to their superior lightweight characteristics and excellent thermal management capabilities. To accurately predict their thermal perfo...
The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DM...
Magnesium phosphate cement (MPC) paste is hardened by the acid–base reaction between magnesium oxide and phosphate. This work collects and evaluates the thermodynamic data at 25 °C and a pressure of 0.1 MPa and establishes the hydration rea...
This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order
This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives i...
Intense chemical weathering in tropical environments poses challenges for conventional geochemical exploration, as primary lithological signatures become heavily altered. Stream sediment geochemistry provides a robust alternative for detecting anomal...
The modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials...
In this study, coral powder with different contents and levels of fineness were incorporated into cement; then, the pore structure of a coral powder–cement slurry was measured using the MIP test at days 3 days and 28, respectively. Neimark&rsqu...
In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fr...
In this paper, we investigate the fractal-fractional Malkus Waterwheel model in detail. We discuss the existence and uniqueness of a solution of the fractal-fractional model using the fixed point technique. We apply a very effective method to obtain...
The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal...
The high-grade uranium deposits in the Xiemisitan area, northwestern China, are genetically associated with the faulting of felsic volcanic or sub-volcanic rocks. Ferric iron alteration indicates that oxidizing hydrothermal fluids percolated through...
The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience....
Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having co...
This paper presents new methods and models for forecasting stock prices and computing hybrid models, combining analytical and neural approaches. First, technical and fractal analyses are conducted and selected stock market indices calculated, such as...
Time series of financial data are both frequent and important in everyday practice. Numerous applications are based, for example, on time series of asset prices or market indices. In this article, the application of fractal interpolation functions in...
In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the mo...
The question addressed by this paper is tackled through a continuum micromechanics model of a 2D random checkerboard, in which one phase is linear elastic and another linear viscoelastic of integer-order. The spatial homogeneity and ergodicity of the...
A three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model’s equilibrium points, as established by the s...
The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F...
In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create ge...
Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which i...
Rice plays an essential role in agricultural production as the most significant food crop. Automated supervision in the process of crop growth is the future development direction of agriculture, and it is also a problem that needs to be solved urgent...
To study the effects of rock models with different fractal dimensions on their mechanical properties and fracture behavior, three representative numerical rock models, including the digital texture model, the Voronoi polygon model, and the Weibull di...
In this paper, we consider the flat FRW spacetime filled with interacting dark energy and dark matter in fractal universe. We work with the three models of dark energy named as Tsallis, Renyi and Sharma–Mittal. We investigate different cosmolog...
It is well established that the introduction of additive manufacturing in various domains has produced significant technological leaps due to the advantages over other manufacturing techniques. Furthermore, additive manufacturing allows the design of...
In this work, using calculations based on the density functional theory, molecular dynamics, non-equilibrium Green functions method, and Monte Carlo simulation, we study electronic and phonon transport in a device based on quasi-fractal carbon nitrid...
In cold regions, hydraulic conductivity is a critical parameter for determining the water flow in frozen soil. Previous studies have shown that hydraulic conductivity hinges on the pore structure, which is often depicted as the pore size and porosity...
A theoretical model for calculating the leakage rate of contact mechanical seals based on the fractal theory of the porous media, which can consider the real seal contact interface and objectively reflect the flow of the interfacial fluid from a micr...
The wetting behavior of shale oil and gas on shale surfaces is determined by the interplay of organic matter (OM), mineral composition, and the intricate pore network structure of the shale. In this paper, the sensitivity responses of the Frenkel&nda...
The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip l...
Accurate estimation of the thermal conductivity of porous materials is crucial for the modeling of heat transfer and energy consumption calculation in energy, aerospace, biomedicine and chemical engineering, etc. The series-parallel model is a simple...
In addressing the issue of strength degradation in saline soil foundations under the salt-freeze coupling effects, a binary medium constitutive model suitable for un-solidified and solidified frozen saline soil is proposed considering both bonding an...
Micro-pore structure has a decisive effect on the physical and mechanical properties of porous materials. To further improve the composition of rock-like materials, the internal relationship between microscopic characteristics (porosity, pore size di...
In this paper, a simple and efficient fractal-based approach is presented for capturing the effects of initial void ratio on the soil-water characteristic curve (SWCC) in a deformable unsaturated soil. In terms of testing results, the SWCCs (expresse...
Tailoring the properties of porous organic materials, such as resorcinol–formaldehyde gels, for use in various applications has been a central focus for many studies in recent years. In order to achieve effective optimisation for each applicati...
In this study, a new nonlinear dynamic model was established for functionally graded material (FGM) beams with layered/porous fractal microstructures, aiming to reveal the cross-scale propagation mechanism of flexural waves under large deflection con...
In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional orde...
In order to further study the internal relationship between the microscopic pore characteristics and macroscopic mechanical properties of cemented tailings backfill (CTB), in this study, mine tailings and ordinary Portland cement (PC32.5) were select...
The revised pore–solid fractal (PSF) model is presented by using the largest inscribed circle-based geometries of squares or cubes to replace the original pore or solid subregions as the new pore or solid phase in porous media. The revised PSF...
In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up...
In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whith...
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