The permeability coefficient and air-entry value of saturated soil are important hydraulic properties, which play an important role in engineering applications. Subsoil supporting foundation is subjected to stress and undergoes deformation; the saturated permeability coefficient of such deformed soil is of practical importance. With the help of fractal theory, based on the different fractal forms of

The fractal characteristic of cement paste has been investigated for decades. In this paper, a systematic study referring to analysis, modeling as well as application is presented with respect to the pore size-dependent fractality of the porous structure in cement paste. In particular, the multiscale fractal dimensions other than the traditional single fractal dimension are analyzed for a measure of

With the increasing demand for energy, heat and mass transfer through porous media has been widely studied. To achieve accuracy in studying the behavior of heat transfer, a good knowledge of the effective thermal conductivity (ETC) of porous materials is needed. Because pore structure dominates the ETC of porous materials and effective stress leads to a change in pore structure, effective stress is

The unsaturated permeability coefficient is of importance to study the behavior of the water seepage and contaminant transport in unsaturated soils. The direct measurement of the unsaturated permeability coefficient is time consuming and laborious. Therefore, indirect approaches are usually applied to obtain the unsaturated permeability coefficient. However, indirect methods still have some drawbacks

In this paper, we study the existence of numerical solution and stability of a chemostat model under fractal-fractional order derivative. First, we investigate the positivity and roundedness of the solution of the considered system. Second, we find the existence of a solution of the considered system by employing the Banach and Schauder fixed-point theorems. Furthermore, we obtain a sufficient condition

This study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for ∇2 of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity

The in-situ foam technology has been extensively applied in the complex reservoir reconstruction since it improves the sweep efficiency by diverting the flow of injected fluids into areas with lower permeability and as a result enhances the oil recovery. The in-situ foam structure inside the pores can significantly affect the sweep efficiency, however, quantitative characterizations on foam structure

The variational theory has triggered skyrocketing interest in the solitary theory, and the semi-inverse method has laid the foundation for the search for a variational formulation for a nonlinear system. This paper gives a brief review of the last development of the fractal soliton theory and discusses the variational principle for fractal Boussinesq-like B(m,n) equation in the literature. The paper

A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed

Grains account for more than 50% of the calories consumed by people worldwide, and military conflicts, pandemics, climate change, and soaring grain prices all have vital impacts on food security. However, the complex price behavior of the global grain spot markets has not been well understood. A recent study performed multifractal moving average analysis (MF-DMA) of the Grains & Oilseeds Index (GOI)

In this paper, two weighted parameterized fractal identities are first proposed, wherein the mappings involved are second-order local fractional differentiable. Based upon these equalities, a series of the weighted parameterized inequalities, which are related to the fractal convex mappings, are then deduced. Moreover, making use of boundedness and (φ,ρ𝜗̂)-Lipschitzian mappings, some error estimates

Gas permeability is an important parameter for gas transport in microporous and nanoporous media. A probability model of gas permeability of fractal porous media with rough surfaces is proposed and numerically simulated by the Monte Carlo technique. This model consists of two gas flow mechanisms: the Poiseuille flow and the Knudsen flow, and can be expressed by structural parameters, such as the pore

Deliverability evaluation plays an important role in the reservoir exploitation. In this study, a new seven-region semi-analytical mathematical model considering the influences of fractal, imbibition and non-Darcy flow is proposed to evaluate the deliverability of multiply-fractured horizontal wells in tight oil reservoirs. The Laplace transformation, perturbation method and Stehfest numerical inversion

Due to a great majority of lung cancer patients dying within one year after being diagnosed with apparent symptoms, developing a diagnostic/monitoring technique for early-stage lung cancer is in critical demand. Conventionally, lung cancer diagnostic approaches are costly, and they increase the health risks caused by invasiveness and radiation hazards. In this work, a new diagnostic technique using

Although the hydraulic features of the tree-like branching network have been widely investigated, the seepage characteristics of the networks have not been studied sufficiently. In this study, the seepage characteristics of porous media embedded with a tree-like branching network with the effects of roughness are studied based on fractal theory. Then, the Kozeny–Carman (KC) constant of the composite

The KdV–Zakharov–Kuznetsov equation is an important and interesting mathematical model in plasma physics, which is used to describe the effect of magnetic field on weak nonlinear ion-acoustic waves. A fractional KdV–Zakharov–Kuznetsov equation in the M-truncated derivative sense is investigated. By taking into account the fractional tanhδ method and fractional sineδ–cosineδ method, larger numbers of

Richards’ equation is a classical differential equation describing water transport in unsaturated porous media, in which the moisture content and the soil matrix depend on the spatial derivative of hydraulic conductivity and hydraulic potential. This paper proposes a nonlocal model and the peridynamic formulation replace the temporal and spatial derivative terms. Peridynamic formulation utilizes a

The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method

The Klein–Gordon–Zakharov equation is an important and interesting model in physics. A fractional Klein–Gordon–Zakharov model is described by employing beta-derivative. Some new solitary wave solutions are acquired by utilizing the fractional rational sinhσ–coshσ method and fractional sechσ method. Some 3D graphs are depicted to elaborate these new solitary wave solutions. The work is very helpful

This paper studies the average trapping time of honeypots on some evolving networks. We propose a simple algorithmic framework for generating networks with Sturmian structure. From the balance property and the recurrence property of Sturmian words, we estimate the average trapping time of our proposed networks with an asymptotic expression 〈T〉t∼Mt(α)2t, where Mt(α) is a bounded expression related to

The stochastic transition behavior of tri-stable states in a fractional-order generalized Van der Pol (VDP) system under multiplicative Gaussian white noise (GWN) excitation is investigated. First, according to the minimal mean square error (MMSE) concept, the fractional derivative can be equivalent to a linear combination of damping and restoring forces, and the original system can be simplified into

A fractal integral identity with the parameter τ related to twice-differentiable mappings is first proposed in this paper. Based on the identity, the parameterized inequalities over the fractal domains are then derived for the mappings whose second-order derivatives in absolute value at certain powers are generalized n-polynomial convex, which is the main purpose of this investigation. Moreover, a

Electrical conductivity is an important physical property of porous media, and has great significance to rock physics and reservoir engineering. In this work, a conductivity model including pore water conductivity and surface conductivity is derived for water-saturated tree-like branching network. In addition, combined with Archie’s law, a general analytical formula for the formation factor is presented

Image denoising has been a fundamental problem in the field of image processing. In this paper, we tackle removing impulse noise by combining the fractal image coding and the nonlocal self-similarity priors to recover image. The model undergoes a two-stage process. In the first phase, the identification and labeling of pixels likely to be corrupted by salt-and-pepper noise are carried out. In the second

Among all probability distributions, power law distribution is an intriguing one, which has been studied by many researchers. However, the derivation of power law distribution is still an inconclusive topic. For deriving a distribution, there are various methods, among which maximum entropy principle is a special one. Entropy of random permutation set (RPS), as an uncertainty measure of RPS, is a newly

A fractal modification of the modified KdV–Zakharov–Kuznetsov equation is suggested and its fractal generalized variational structure is established by means of the semi-inverse method. Furthermore, the obtained fractal generalized variational structure is discussed and verified through the two-scale transform from another dimension field in detail. The obtained fractal generalized variational structure

In this paper, exact traveling wave solutions of space-time fractional simplified modified Camassa–Holm (mCH) equation are investigated by the bifurcation theory. The phase portraits of the equation are obtained with different parameter conditions. By analyzing different orbits, periodic wave, kink, anti-kink, burst wave, bright and dark solitary solutions of the equation are acquired. Finally, numerical

The alignment or mapping of Deoxyribonucleic Acid (DNA) reads produced by the new massively parallel sequencing machines is a fundamental initial step in the DNA analysis process. DNA alignment consists of ordering millions of short nucleotide sequences called reads, using a previously sequenced genome as a reference, to reconstruct the genetic code of a species. Even with the efforts made in the development

This study presents the modified form of the homotopy perturbation method (HPM), and the Yang transform is adopted to simplify the solving process for the Kuramoto–Sivashinsky (KS) problem with fractal derivatives. This scheme is established by combining the two-scale fractal scheme and Yang transform, which is very helpful to evaluate the approximate solution of the fractal KS problem. Initially,

A vibration system with discontinuities has triggered off rocketing interest in various fields including mechanical engineering, physics, and mathematics because it has many striking and amazing properties which cannot be unexplained by traditional vibration theory. This paper studies the problem using the energy conservation frame in a fractal time. A variational formulation is developed, and its

In this work, we have given an analogical method for estimating the fractal dimension for three-dimensional fracture tortuosity (3D-FT). The comparison and error analysis of analogical and rigorous methods on fractal dimension for 3D-FT were carried out in this work. The fractal dimension DT−R for 3D-FT from the proposed analogical method is the function of 3D fracture average tortuosity (τav) and

Given 0

This paper proposes an innovative method to take advantage of Blockchain Convolutional Neural Networks (BCNNs) in Emotion Recognition (ER). Based on Artificial Intelligence, this proposal uses audio-visual emotion patterns to determine psychiatric profiles to attend to the most urgent as a priority. BCNN architectures were used to identify emergency patterns. The results indicate that the proposed

Zeng and Xi introduced the Hausdorff dimension of a family of networks and investigated the dimensions of touching networks. In this paper, using the self-similarity and induction we obtain the Hausdorff dimension of flower networks and Hanoi graphs, which are not touching networks.

We introduce a class of sets defined by digit restrictions in ℝ2 and study its fractal dimensions. Let ES,D be a set defined by digit restrictions in ℝ2. We obtain the Hausdorff and lower box dimensions of ES,D. Under some condition, we gain the packing and upper box dimensions of ES,D. We get the Assouad dimension of ES,D and show that it is 2 if and only if ES,D contains arbitrarily large arithmetic

The hyper-Wiener index on a graph is an important topological invariant that is defined as one half of the sum of the distances and square distances between all pairs of vertices of a graph. In this paper, we develop the discrete version of finite pattern to compute the accurate formulas of the hyper-Wiener indices of the Sierpiński skeleton networks.

In this study, we proposed a novel approach for modeling the dynamics of a three-agent financial bubble using the fractal-fractional (FF) derivative of the Caputo sense. This new concept was developed to deal with the complex geometry of any dynamical system, and it utilizes both the fractional derivative for the order and the fractal term for the order of the independent variables. The model was investigated

The marine predator algorithm (MPA) is the latest metaheuristic algorithm proposed in 2020, which has an outstanding merit-seeking capability, but still has the disadvantage of slow convergence and is prone to a local optimum. To tackle the above problems, this paper proposed the flexible adaptive MPA. Based on the MPA, a flexible adaptive model is proposed and applied to each of the three stages of

The hydro-mechanical coupling behavior of the fractured rock is constitutive in accurately modeling the seepage properties such as permeability and porosity. In this work, the stress-dependent models for permeability and porosity of the fractured rock are proposed by employing the fractal geometry theory and the two-part Hooke’s model (TPHM). The proposed models for the permeability and porosity are

We analyze the local geometric structure of self-similar sets with open set condition through the study of the properties of a distinguished family of spherical neighborhoods, the typical balls. We quantify the complexity of the local geometry of self-similar sets, showing that there are uncountably many classes of spherical neighborhoods that are not equivalent under similitudes. We show that at a

Abnormal detection of wind turbine converter (WT) is one of the key technologies to ensure long-term stable operation and safe power generation of WT. The number of normal samples in the SCADA data of WT converter operation is much larger than the number of abnormal samples. In order to solve the problem of low abnormal data and low recognition rate of WTs, we propose a sample enhancement method for

Steam coal is the blood of China industry. Forecasting steam coal prices accurately and reliably is of great significance to the stable development of China’s economy. For the predictive model of existing steam coal prices, it is difficult to dig the law of nonlinearity of power coal price data and with poor stability. To address the problems that steam coal price features are highly nonlinear and

Time-delayed fractional-order systems are crucial in modeling and analyzing various physical systems, ranging from mechanical and electrical systems to biological and environmental ones. While estimators play an inevitable role in achieving high accuracy in controlling nonlinear systems, control techniques intended for time-delayed fractional-order systems struggle to estimate uncertainties within

For the problem of class-imbalance in the operation monitoring data of wind turbine (WT) pitch connecting bolts, an improved Borderline-SMOTE oversampling method based on “two-step decision” with adaptive selection of synthetic instances (TSDAS-SMOTE) is proposed. Then, TSDAS-SMOTE is combined with XGBoost to construct a WT pitch connection bolt fault detection model. TSDAS-SMOTE generates new samples

In this work, we analyze the high-frequency time series of the deposits collected from the systemic biggest Greek banks during the recent economic crisis in Greece. Our focus has been to reveal hidden fractal and periodic patterns using a hybrid approach, which combines correlation and frequency analysis of the original and difference series in a synergistic manner. We find that during the first period

This investigation aims to investigate the pine wilt disease model (PWDM) employing hybrid bio-inspired algorithm. The artificial neural networks-based genetic algorithm (ANNs-GA) as global search and sequential quadratic programming (SQP) serve as local search framework. The model consists of two populations, i.e. host (h) and vector (v). There are four classes in host population representing susceptible

Almost every natural process is stochastic due to the basic consequences of nature’s existence and the dynamical behavior of each process that is not stationary but evolves with the passage of time. These stochastic processes not only exist and appear in the fields of biological sciences but are also evident in industrial, agricultural and economical research datasets. Stochastic processes are challenging

This paper intends to estimate the box dimension of the Weyl–Marchaud fractional derivative (Weyl–M derivative) for various choices of continuous functions on a compact subset of ℝ. We show that the Weyl–M derivative of order γ of a continuous function satisfying Hölder condition of order μ also satisfies Hölder condition of order μ−γ and the upper box dimension of the Weyl–M derivative increases at

Stress field is a key external factor affecting the thermodynamic properties of rock in many scientific and engineering fields ranging from geoscience to practical problems in geothermal resources, oil and gas exploitation, mineral exploitation, etc. In this work, the stress-dependent models for the effective thermal conductivity of fractured rock are proposed by combining the fractal geometry theory

This paper intends to estimate the box dimension of the Weyl–Marchaud fractional derivative (Weyl–M derivative) for various choices of continuous functions on a compact subset of ℝ. We show that the Weyl–M derivative of order γ of a continuous function satisfying Hölder condition of order μ also satisfies Hölder condition of order μ−γ and the upper box dimension of the Weyl–M derivative increases at

Stress field is a key external factor affecting the thermodynamic properties of rock in many scientific and engineering fields ranging from geoscience to practical problems in geothermal resources, oil and gas exploitation, mineral exploitation, etc. In this work, the stress-dependent models for the effective thermal conductivity of fractured rock are proposed by combining the fractal geometry theory

Much information on the structural properties and some relevant dynamical aspects of a graph can be provided by its normalized Laplacian spectrum, especially for those related to random walks. In this paper, we aim to present a study on the normalized Laplacian spectra and their applications of weighted level-4 Sierpiński graphs. By using the spectral decimation technique and a theoretical matrix analysis

In this paper, we derive a new fractal modified Benjamin–Bona–Mahony equation (MBBME) that can model the long wave in the fractal dispersive media of the optical illusion field based on He’s fractal derivative. First, we apply the semi-inverse method (SIM) to develop its fractal generalized variational principle with the aid of the fractal two-scale transforms. The obtained fractal generalized variational

In the era of 5G/B5G, computing-intensive, delay-sensitive applications such as virtual reality inevitably bring huge amounts of data to the network. In order to meet the real-time requirements of applications, Mobile Edge Computing (MEC) pushes computing resources and data from the centralized cloud to the edge network, providing users with computing offload technology. However, the mismatch between

Visual Question Answering (VQA) is a multimodal task, which requires understanding the information in the natural language questions and paying attention to the useful information in the images. So far, the solution of VQA tasks can be divided into grid-based methods and bottom-up-based methods. The grid-based method directly extracts the semantic features of the image by leveraging the convolution

This paper proposed a method for the fractal characterization of the three-dimensional (3D) fracture tortuosity (DT3) in coal based on CT scanning experiment. The methodology was deduced in detail, and the values of DT3 of four coal samples were calculated by the rigorous derivation equation established by Feng and Yu. The values of DT3 by the proposed method fit the relation of DT3 versus the fractal

Applying the local fractional integrals, a generalized identity involving the local second-order differentiable mappings is first developed in this paper. A series of fractal integral inequalities pertaining to Simpson type, for the mappings whose local second-order derivatives are generalized (s,P)-convex in absolute value at some power, are then deduced by the discovered identity. Finally, from an

This paper has investigated the predictability of the top 10 cryptocurrencies’ price dynamics, ranked by their daily market capitalization and trade volume, via the information theory quantifiers. Our analysis considers the Complexity-entropy causality plane to study the temporal evolution of the price of these cryptocurrencies and their respective locations along this 2D map, bearing in mind after

In this paper, we study the approximation orders of a real number x∈(0,1) by the partial sums of its β-expansions as β varies in the parameter space {β∈ℝ:β>1}. More precisely, letting Sn(x,β) be the partial sum of the first n items of the β-expansion of x, we prove that for any real number x∈(0,1), the approximation order of x by Sn(x,β) is β−n for Lebesgue almost all β>1. Moreover, we obtain the size

In this paper, the integral of classical fractal interpolation function (FIF) and A-fractal function is explored for both the cases of constant and variable scaling factors. The definite integral for the classical FIF in the closed interval of ℝ is estimated. The novel notion of affine-quadratic FIF is introduced and integrated for both constant and variable scaling factors. It is demonstrated that