Fractal and Fractional, Volume 9, Issue 8

Fractal theory provides a powerful tool for quantifying complex geometric patterns such as concrete cracks. The box-counting method is widely employed for fractal dimension (FD) calculation due to its intuitive principles and compatibility with image...

Using the newly introduced, by the author, basic complex and hybrid complex rheologic models of the fractional type, the dynamics of a series of mechanical rheologic discrete dynamical systems of the fractional type (RDDSFT) of rheologic oscillators...

We are especially interested in the general framework and ability of a semi-analytic method (SAM) to use the trigonometric basis function (TBF) in different domains. Moreover, the stabilizing effect of increasing boundary nodes on the convergence of...

This paper presents a comprehensive dynamical analysis of a nonlinear oscillator subjected to both deterministic and stochastic excitations. Utilizing a diverse suite of analytical tools—including phase portraits, Poincaré sections, Lyap...

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretace...

The novelty herein pertains to a class of fractional differential equations involving the Hadamard fractional derivative of higher order. Our investigation encompasses the fractional integral operator of a logarithmic function. The mathematical tools...

The inherent randomness and concealment of rumors in social networks exacerbate their spread, leading to significant societal instability. To explore the mechanisms of rumor propagation for more effective control and mitigation of harm, we propose a...

Rod pump systems are complex nonlinear processes, and conventional efficiency prediction methods for such systems typically rely on high-order fractional partial differential equations, which severely constrain real-time inference. Motivated by the i...

This paper studies the large deviation principle (LDP) of a class of Hilfer fractional stochastic McKean–Vlasov differential equations with multiplicative noise. Firstly, by making use of the Laplace transform and its inverse transform, the sol...

This study presents a comprehensive grayscale texture analysis framework for investigating the microstructural evolution of cement-based materials during hydration. High-resolution X-ray computed tomography (X-CT) slice images were analyzed across fi...

This paper presents a finite element implementation of a fractional rheological consolidation model in ABQUS, in which the fractional Merchant model governs the mechanical behavior of the soil skeleton, and the water flow is controlled by the fractio...

This paper introduces an innovative artificial neural networks-based analytical solver for fractional partial differential equations (fPDEs), combining neural networks (NNs) with symbolic computation. Leveraging the powerful function approximation ab...

This paper investigates a novel class of weighted fuzzy fractional Volterra–Fredholm integro-differential equations (FWFVFIDEs) subject to integral boundary conditions. The analysis is conducted within the framework of Caputo-weighted fractiona...

Microseismic monitoring has become a critical technology for hydraulic fracturing in unconventional oil and gas reservoirs, owing to its high temporal and spatial resolution. It plays a pivotal role in tracking fracture propagation and evaluating sti...

Fractal and fractional theories have developed over several decades and have gradually grown in popularity, with significant applications in geotechnical engineering [...]

The nanoporous structure of coal is crucial for the occurrence and development of coalbed methane (CBM). This study, leveraging the combined characterization of atomic force microscopy (AFM) and Gwyddion software (v2.62), investigated six anthracite...

The dynamic process of water depletion plays a critical role in both surface coalbed methane (CBM) development and underground gas extraction, reshaping water–rock interactions and inducing complex permeability responses. Addressing the limited...

The geological structural complexity and microscale heterogeneity of shale reservoirs, characterized by the brittleness index and natural fracture density, exert a decisive effect on hydraulic fracturing’s effectiveness. However, the mechanisms...

Understanding the intrinsic relationship between microscopic structures and macroscopic mechanical properties of rock under freeze–thaw (F-T) conditions is essential for ensuring the safety and stability of geotechnical engineering in cold regi...

In the field of deep learning, the traditional Vision Transformer (ViT) model has some limitations when dealing with local details and long-range dependencies; especially in the absence of sufficient training data, it is prone to overfitting. Structu...

This study focuses on the complex pore structure and pronounced heterogeneity of tight sandstone reservoirs in the Linxing area of the Ordos Basin and develops a multi-scale quantitative characterization approach to investigate the coupling mechanism...

Coal mining disturbance induces progressive damage and fracturing in overlying rock (OLR), forming a complex fracture network. This process triggers groundwater depletion, ecological degradation, and severely compromises mine safety. Based on field d...

In this study, we propose a novel metaheuristic algorithm named Kangaroo Escape optimization Technique (KET), inspired by the survival-driven escape strategies of kangaroos in unpredictable environments. The algorithm integrates a chaotic logistic en...

This paper considers the multi-term subdiffusion equation with weakly singular solutions. In order to use sparser meshes near the initial time, a novel scheme (which we call the corrected L1 scheme) on graded meshes is constructed to estimate the mul...

In recent years, we have abstracted physical fractal space from biological structures and movements within living organisms, revealing the profound intrinsic connections between fractional order time and fractional-dimensional space, and providing pa...

Deep shale gas reservoirs are vital sources of unconventional natural gas and present unique challenges for exploration and development due to their multiscale flow characteristics and elastoplastic deformation behavior of reservoir rocks. Accurately...

In this work, we prove some fixed point theorems in rectangular $G_b$-metric space, which is the generalization of rectangular metric space and $G_b$-metric space. Moreover, we give some examples to support our theoretical findings. Finally, using our main...

A significant application of the proportional–integral (PI) controller in the automotive sector is in electric motors, particularly brushless direct current (BLDC) motors utilized in electric vehicles (EVs). This paper presents a high-performan...

Shale pore architecture governs gas storage capacity, permeability, and production potential in reservoirs. Therefore, this study systematically investigates the pore structure features and influencing factors of the Niutitang Formation shale from th...

Rapid and large-scale monitoring of soil copper levels enables the quick identification of areas where copper concentrations significantly exceed safe thresholds. It allows for selecting regions that require treatment and protection and is essential...

This study employs the improved modified extended tanh method (IMETM) to derive exact analytical solutions of a higher-order nonlinear Schrödinger (HNLS) model, incorporating $\beta$-fractional derivatives in both time and space. Unlike classical...

The feature selection (FS) procedure is a critical preprocessing step in data mining and machine learning, aiming to enhance model performance by eliminating redundant features and reducing dimensionality. The Energy Valley Optimizer (EVO), inspired...

Based on the spatial compact finite difference (SCFD) method, an improved high-order temporal accuracy scheme for high-dimensional time-fractional diffusion equations (TFDEs) is presented in this work. Combining the temporal piecewise quadratic inter...

In this work, we explore Wirtinger-type inequalities involving tempered Ψ-Caputo fractional derivatives by utilizing Taylor’s formula. We establish more general inequalities for the same operator in $L_p$ norms for $p>1$ by using Hölder&...

Organic matter plays a vital role in shale reservoirs as both a hydrocarbon storage medium and migration pathway. However, the quantitative relationship between the microstructural features of organic matter and the macroscopic mechanical and failure...

The objective of this study is to evaluate the trabecular structure in hypodivergent individuals using fractal analysis, with a particular focus on specific mandibular regions. This study aims to assess the impact of hypodivergent growth patterns on...

This paper investigates weighted Milne-type ($\mathcal{M}-\mathfrak{t}$) inequalities within the context of Riemann–Liouville ($\mathfrak{R}-\mathfrak{L}$) fractional integrals. We establish multiple versions of these inequalities, applicable to different function categories, su...

Rolling bearings are prone to failure, meaning that research on intelligent fault diagnosis is crucial in relation to this key transmission component in rotating machinery. The application of deep learning (DL) has significantly advanced the developm...

The fractional PDE-ODE coupled system with Neumann boundary condition is considered in this paper. We design a boundary state feedback controller using the Backstepping method to stabilize the considered system. According to operator semigroup theory...

In this manuscript, we study a class of nabla fractional difference equations with summation boundary conditions that depend on a parameter. We construct the Green’s function related to the linear problem and we deduce some of its properties. F...

This work introduces a new family of multivariate hybrid special polynomials, motivated by their growing relevance in mathematical modeling, physics, and engineering. We explore their core properties, including recurrence relations and shift operator...

In the field of deep learning, the design of optimization algorithms and neural network structures is crucial for improving model performance. Recent advances in medical image analysis have revealed that many pathological features exhibit fractal-lik...

This paper focuses on the problem, claimed in some works, of the non-existence of finite-time stable equilibria in nonlinear fractional differential equations. After dividing the equilibrium point into the initial equilibrium point and the finite-tim...

Fractional differential equations constitute an important research direction in modern mathematics and applied sciences [...]

This paper focuses on the numerical modeling of drug diffusion in biological tissues using fractional time-dependent parabolic equations with non-local boundary conditions. The model includes a Caputo fractional derivative to capture the non-local ef...

Community detection in complex networks plays a pivotal role in modern scientific research, including in social network analysis and protein structure analysis. Traditional community detection methods face challenges in integrating heterogeneous mult...

With the rapid proliferation of real-time digital communication, particularly in multimedia applications, securing transmitted image data has become a vital concern. While chaotic systems have shown strong potential for cryptographic use, most existi...

In this study, we present two novel subclasses of bi-univalent functions defined in the open unit disk, utilizing Liouville–Caputo fractional derivatives. We find constraints on initial Taylor coefficients $|c_2|$, $|c_3|$ for functions in these subc...

Research on reliability control for enhancing power systems under random loads holds significant and undeniable importance in maintaining system stability, performance, and safety. The primary challenge lies in determining the reliability index while...

This study addresses the practical stability analysis of Riemann-Liouville fractional-order nonlinear systems with time delays. We first establish a rigorous formulation of initial conditions that aligns with the properties of Riemann-Liouville fract...