Fractal and Fractional, Volume 9, Issue 4

Pore structure plays a critical role in evaluating shale “sweet spots”. Compared to marine shale, lacustrine shale has more diverse lithofacies types and greater heterogeneity in pore structure due to frequently changing environmental con...

The successful exploration and development of shale oil in the clay-rich Gulong shale have sparked increased research into the influence of clay minerals on shale reservoirs. However, compared to chlorite in sandstones, limited studies have focused o...

Fractional variable order systems with unusual dynamics in the order are a little-studied topic. In this study, we present three examples of very simple fractional systems with unusual dynamics in the derivative order. These cases involve different a...

The pore structure of reservoir rocks was a crucial factor affecting hydrocarbon production. Accurately characterized the micropore structure of different types of rock reservoirs was of great significance for unconventional natural gas exploration....

High-tech industries are of strategic importance to the national economy, and Beijing has been designated as a science and technology innovation center by the State Council. Accurate analysis of its added value is crucial for technological developmen...

In this article, we study a fractional lower-order differential equation, $-D_{0+}^{\alpha }{\rm Y}\left(\xi \right)+\mathrm{a}\left(\xi \right){\rm Y}\left(\xi \right)=\mathrm{y}\left(\xi \right),\xi \in (0,1),\alpha \in (1,2),$ with a Dirichlet-type boundary condition, where $\mathrm{a}\left(\xi \right)\in L^1[0,1]$ permits...

Bayoud disease, caused by Fusarium oxysporum f. sp. albedinis, is a major threat to date palm trees. It leads to lower crop yields, financial losses, and decreased biodiversity. The complexity of the disease presents challenges to effective disease m...

In this research article, we investigate a three-dimensional dynamical system governed by fractal-fractional-order evolution differential equations subject to terminal boundary conditions. We derive existence and uniqueness results using Schaefer&rsq...

This paper presents an advanced simulation-based investigation of tumor growth and chemical diffusion in biological tissues, using $\vartheta$-fractional stochastic integral equations. Based on the theoretical framework developed in [Fractal Fract. 20...

Fractal analysis was used to characterize the organic matter nanopore structure in tectonically deformed shales, providing insights into the heterogeneity and complexity of the pore network. Shale samples from different tectonic deformation styles (u...

On the one hand, convex functions are important to derive rigorous convergence rates, and on the other, synchronous functions are significant to solve statistical problems using Chebyshev inequalities. Therefore, fractional integral inequalities invo...

A total of 108 maximum Kolmogorov entropy (S_K) values, calculated by means of chaos theory, are obtained from 108 time series (TSs) (each consisting of 28,463 hourly data points). The total TSs are divided into 54 urban meteorological (temperature (T...

Concrete materials exposed to sulfate-rich geological environments are prone to structural durability degradation due to chemical erosion. Silane-based protective materials can enhance the durability of concrete structures under harsh environmental c...

This paper proposes an innovative method that combines the homotopy analysis method with the Jafari transform, applying it for the first time to solve systems of fractional-order linear and nonlinear differential equations. The method constructs appr...

In this paper, a counter-example based on a realistic initial condition invalidates the usual approach related to the so-called physical initial condition of the Caputo derivative used to solve fractional-order Cauchy problems. Due to Infinite State...

This paper introduces a novel fractional Susceptible-Infected-Recovered ($\mathbb{SIR}$) model that incorporates a power Caputo fractional derivative (PCFD) and a density-dependent recovery rate. This enhances the model’s ability to capture memory effects and r...

The pore–fracture structure of ultra-deep coal is critical for evaluating resource potential and guiding the exploration and development of deep coalbed methane (CBM). In this study, a coal sample was obtained from the Gaogu-4 well at a depth o...

This paper investigates the well-posedness of analytical solutions to fractional quadratic differential equations, which involve generalized fractional integrals with respect to other functions. The nonlinear components f and h depend on spatial vari...

Multiple-stream deep learning (DL) models are typically used for multiple-modality datasets, with each model extracting favorable features from its own modality dataset. Through feature fusion, multiple-stream models can generally achieve higher reco...

This article presents a computational analysis of approximate solutions for the time-fractional nonlinear Kawahara problem (KP) and the modified Kawahara problem (modified KP). This study utilizes the natural homotopy transform scheme (NHTS), which i...

In this work, the novel general formula for a time-dependent nuclear reactor system of equations with delayed neutron effect has been formulated using a fractional calculus model. We explore the properties of this model, including two analytical appr...

This study focuses on a novel parameterized Wigner distribution, which is an organic integration of the free metaplectic Wigner distribution and the $\mathbf{K}$-Wigner distribution. We style this as the free metaplectic $\mathbf{K}$-Wigner distribution (FMKWD) and invest...

This paper investigates the fractional-order characteristics of the stator and rotor windings of a synchronous generator. Utilizing mechanism-based modeling methodology, it pioneers the derivation of the fractional-order voltage equations for a synch...

This research examines a fractional partial advection–dispersion model, incorporating both mobile and immobile components, employing the Hilbert reproducing algorithm under an appropriate Neumann constraint condition. To effectively formulate t...

With the rapid expansion of the internet and accelerated information dissemination, rumors pose a significant threat to social stability. Effective rumor control requires a thorough understanding of propagation mechanisms. This study develops a Caput...

Finite-time synchronization depends on the initial conditions of the system in question. However, the initial conditions of an actual system are often difficult to estimate or even unknown. Therefore, a more valuable and pressing problem is fixed-tim...

The static shift effect is a distortion in electromagnetic data that severely impacts exploration results. Traditional static effect correction methods are often ineffective, prone to overcorrection or undercorrection, and make it difficult to accura...

In this paper, the authors consider a problem with comprehensive properties in terms of form and content in the space ${\mathcal{L}}_2\left[\left(a,b\right)\times \left(\mathrm{c},\mathrm{d}\right)\right]\times C\left[0,T\right],T<1$. In terms of time form, we assume that the time phase delay is implicitly contained in a nonlinear...

The stability of differential equations is one of the most important aspects to consider in dynamical system theory. Chaotic systems were classified according to stability as multi-stable systems; systems with a single stable equilibrium; bi-stable s...

Taylor expansion is a remarkable tool with broad applications in analysis, science, engineering, and mathematics. In this manuscript, we derive a proof of generalized Taylor expansion for polynomials and write its particular case in symmetric quantum...

The long-term effects of dry–wet cycles induced by seasonal rainfall significantly influence the creep behavior of sliding zone soft rocks, contributing to landslide occurrence. Understanding this aspect is crucial for predicting and mitigating...

This paper first examines the evolution of pore-size distribution (PSD) in four types of reconstituted clays during one-dimensional (1D) compression, utilising mercury intrusion porosimetry. Central to this work, fractal theory is then applied to qua...

Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order...

With the increasing construction of engineering structures on soft soils, accurately assessing their consolidation behavior has become crucial. To address this, Terzaghi’s one-dimensional consolidation model was revisited. The elastic behavior...

In order to explore the influence of grain size on the mechanical properties of unbolted and bolted composite rock masses, uniaxial compression tests were carried out on unbolted and bolted composite rock masses of different grain sizes. The characte...

The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that all...

The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the exi...

We discuss the existence criteria and Ulam–Hyers stability for solutions to a nonlocal integral boundary value problem of nonlinear coupled Hilfer–Hadamard-type fractional Langevin equations. Our results rely on the Leray–Schauder a...

Significant new progress has been made in nonlinear integrable systems with Riesz fractional-order derivative, and it is impressive that such nonlocal fractional-order integrable systems exhibit inverse scattering integrability. The focus of this art...

This work investigates the fractional Dirac system that has transmission conditions, and its boundary condition contains an eigenparameter. Defining a convenient inner product space and a new operator that has the same eigenvalues as the considered p...

In this study, we introduce an innovative approach for addressing fractional partial differential equations (fPDEs) by combining Monte Carlo-based physics-informed neural networks (PINNs) with the cuckoo search (CS) optimization algorithm, termed PIN...

This paper focuses on the application of fractional calculus techniques in the identification and control of multivariable (multiple input—multiple output) systems (MIMO). By considering a previously reported experimental set-up similar to a gr...

In the Southeastern Ordos Basin, the Chang 2 low-permeability sandstone reservoir of the Triassic Yanchang Formation is a typical heterogeneous reservoir. Quantitatively characterizing and analyzing its complex pore throat structure has become crucia...

The fractal characteristics of soil microstructures, including the size, distribution, and dynamic evolution process of soil particles, cracks, and intergranular pores, are important factors influencing the macroscopic physical properties of soils. Q...

To effectively mitigate resonance in dual-inertia servo inverter systems with a lightweight flexible shaft or coupling, the precise modeling of the dual-mass mechanism is essential. This paper proposes a fractional-order modeling and identification m...

Uniaxial compression tests were conducted on coal samples subjected to different dry–wet cycling treatments to investigate the damage and degradation mechanisms of coal samples under the dry–wet cyclic action of acidic, high-salinity solu...

Based on the uniaxial compression tests and in situ CT scanning experiments of lignite with different dehydration times and the fractal theory, this paper qualitatively and quantitatively investigated the influence of the dehydration effect on the ev...

The study of vibration equations of large membranes is crucial in various scientific and engineering fields. Analyzing the vibration equations of bridges, roofs, and spacecraft structures helps in designing structures that resist excessive oscillatio...

This work integrates the fast Alikhanov method with a compact scheme to solve the time-fractional Kuramoto–Sivashinsky (KS) equation with the generalized Burgers’ type nonlinearity. Initially, the Alikhanov algorithm, designed to handle t...

Against the backdrop of increasingly severe global climate challenges, various industries are in urgent need of developing materials that can both improve performance and reduce carbon emissions. In this study, carbon dioxide nanobubble water (CO₂NBW...