Fractal and Fractional, Volume 10, Issue 8

Geochemical gold datasets from shear zone-hosted systems frequently contain extreme outliers that distort statistical structure, shift population boundaries, and undermine the reliability of concentration–area (C–A) fractal modeling. Conv...

Fractures exhibit complex spatial structures and multiscale geometric characteristics, and their accurate characterization is fundamental to reservoir evaluation, fluid migration analysis, and rock mechanics. To address the limitations of single-scal...

A fractional-order image enhancement and fractal complexity-guided fusion method was developed to improve weak fault representation and introduce complexity-aware priors into dissolved gas analysis (DGA)-based diagnosis of oil-immersed power transfor...

Active Infrared Thermography is widely used to characterize laser–tissue interactions, yet quantitative extraction of non-Fourier transport parameters often relies on lock-in demodulation or computationally intensive inverse procedures. Here we...

Closed-form Caputo gradients in critical-state stress-fractional plasticity have relied on the polynomial Modified Cam-Clay surface. We extend them to the non-polynomial teardrop bounding surface by defining the operator as a Caputo derivative in the...

Underground coal mining can induce deformation and failure of overlying strata and ground surface, which seriously endangers the safety of human life and property. During mining, the immediate roof rock successively experiences initial caving (fixed...

Ultrasonic attenuation in particle–cementitious heterogeneous media results from the coupled effects of matrix memory dissipation and particle-induced random heterogeneity, which cannot be readily distinguished using conventional homogeneous-me...

In this paper, motivated by the modified Tremblay fractional differential operator and the normalized generalized Bessel–Maitland function, we introduce the generalized Bessel–Maitland–Tremblay function via the Hadamard product tran...

Permeability models are essential for quantitatively describing coal permeability evolution and predicting gas migration during deep mining. Deep coal subjected to mining disturbance commonly exhibits pronounced nonlinear changes in permeability, lim...

This article introduces the concept of proximal enriched contractions for nonself mappings by integrating the enrichment technique of Berinde and Păcurar with the relation-theoretic approach of Alam and Imdad. The existence of best proximity poi...

The paper investigates the asymptotic stability for the control of systems described by multi-order fractional differential equations. By utilizing generalized Lyapunov functions and the Kalman–Yakubovich–Popov lemma, frequency-domain cri...

Nonlinear electromagnetic wave propagation in complex plasma environments has attracted considerable attention due to its important applications in nonlinear optics, plasma physics, space science, and communication technologies. In the present study,...

This paper presents a novel fractional-order hybrid observer framework for robust sensorless control of brushless DC (BLDC) motor drives in unmanned aerial vehicle (UAV) propulsion systems, addressing the fundamental limitations of conventional integ...

Conventional integer-order parameter designs of grid-forming inverters provide limited degrees of freedom for impedance adjustment, motivating the exploration of additional approaches for flexible impedance reshaping across different frequency ranges...

Let $\mathcal{G}$ be a homogeneous Lie group of dimension $\varkappa$. In this article, we investigate the mapping properties of the Wolff-type potential ${\mathcal{W}}_{\vartheta ,2}$ on $\mathcal{G}$, associated with a homogeneous quasi-norm, and show that it coincides, up to an explicit dime...

In this paper, the new fractal modified Zakharov–Kuznetsov equation (fmZKe) defined on Cantor sets is investigated. The fmZKe is a non-differentiable model that arises naturally in mathematical physics, nonlinear wave theory, and plasma physics...

Time-fractional diffusion equations describe subdiffusive transport in heterogeneous media, but their numerical treatment is complicated by the nonlocal Caputo derivative and by the weak singularity that the solution develops at the initial time. We...

This work addresses the Ulam–Hyers stability of mild solutions of fractional noninstantaneous evolution nonlinear equations subject to noninstantaneous impulses in the Banach space through an approach based on the measure of noncompactness. Mil...

Time delays are inherently present in active control systems as a consequence of sensor acquisition, communication lags, and actuator dynamics, and their impact on system behavior cannot be overlooked. This paper examines the effect of delayed displa...

Three-dimensional Riemann–Liouville time-fractional integro-differential equations provide useful prototype models for diffusion and transport processes with temporal memory and weakly singular hereditary effects. Their numerical solution is ch...

Complex surfaces exhibit hierarchical morphological organizations that cannot be fully described by conventional roughness parameters alone. In this study, a fractal–statistical framework is proposed to elucidate the substrate-controlled morpho...

Tight sandstone reservoir effectiveness is governed not by pore volume alone, but by the storage and flow contributions of different pore-throat scales, their structural complexity, and their three-dimensional connectivity. This study investigates ti...

This paper investigates how opinion dynamics with memory effects and random communication uncertainties achieve consensus in an inhomogeneous Hegselmann–Krause (H-K) model. The Caputo fractional derivative is introduced to describe the influenc...

Let $\mathcal{A}$ denote the class of functions $g\left(z\right)=z+{\sum }_{k=2}^{\infty }{a}_k{z}^k$ analytic and normalized in $\mathbb{U}=\{z:|z|<1\}$, and let $D=\{g\in \mathcal{A}:|g^{″}\left(z\right)|\le 1,z\in \mathbb{U}\}$. We give a short, self-contained proof that D consists entirely of univalent functions by a dir...

Integrated Modular Avionics (IMA) integrates safety-critical functions on shared computing and network resources, creating coupling channels through which a local fault may escalate into a catastrophic system-level scenario. This study develops a gra...

This paper investigates the finite-time stabilization of fractional-order impulsive switched neural networks subject to actuator saturation. Such systems combine memory-dependent fractional dynamics, mode switching, impulsive updates, and bounded con...

We investigate the asymptotic behavior of a Timoshenko beam system in which the free end carries a tip mass subject to a restoring spring force and a tempered Caputo fractional damping force with parameter $\eta >0$ (the case $\eta =0$ is left as an o...

This paper investigates the qualitative and topological behavior of random solutions for a class of partial fractional random differential equations governed by the Darboux problem. Unlike classical configurations that rely on bounded or finite delay...

In this study, random-order FDEs are studied with a focus on the variability of their solutions and random orders when the order of differentiation is governed by a probability distribution. Fractional differential equations (FDEs) offer a generalize...

Deep shale reservoirs in the tectonically complex margin of the southern Sichuan Basin have experienced multistage deformation, resulting in strong spatial heterogeneity of the present-day geostress field. However, the influence of stress heterogenei...

Deep shale reservoirs in the southern Sichuan Basin have undergone strong tectonic reworking, producing pore structure heterogeneity that affects reservoir quality and hydrocarbon preservation. In this study, shales with different deformation intensi...

Impacted mandibular third molar surgery is one of the most common procedures in oral and maxillofacial surgery, and an accurate preoperative assessment of surgical difficulty remains clinically important. The Pederson difficulty index is widely used...

In this paper, we investigate the existence of positive solutions for a class of p-Laplacian tempered Riemann–Liouville fractional equations involving signed measures and sign-changing perturbations with Riemann–Stieltjes boundary conditi...

The marine and continental transitional facies coal of the Longtan Formation in western Guizhou Province is a key area for coalbed methane (CBM) exploration and development in Southwest China and has numerous resources; however, the exploration and d...

Fiber-reinforced high-water-resistance concrete backfill (FHWCB) is a rapid-setting cementitious backfill system used for underground support and backfilling, but its stability is strongly affected by mixture water content and fiber dispersion. This...

The Yang local fractional calculus was developed to analyze discontinuous mappings. The results obtained within this framework are equally useful in the classical sense. The study of integrals and their approximation rules is an interesting field of...

Understanding the anisotropic mechanical behavior and pore–fracture structure (PFS) evolution of bedded coal under mining disturbance is critical for gas extraction and hazard prevention in deep coal mining. This study employed low-field nuclea...

This paper proposes a novel susceptible–infected–susceptible (SIS) epidemic model incorporating a fractional-order term and white-noise perturbations. Several analytical results concerning its dynamical behavior are established. Firstly,...

Hard roof strata in deep coal mines commonly cause rib failure and roof collapse, restricting extraction efficiency. This study employs theoretical analysis, numerical simulation, and field experiments to investigate the fractal evolution of damage i...

Existing analytical solutions for Brownian coagulation of fractal aggregates typically assume a constant geometric standard deviation during derivation to achieve closed-form expressions. This simplification introduces notable systematic deviations a...

Nonlocal circumstances in genetic engineering are crucial as they pertain to the understanding of genetic material. When these conditions are associated with differential integral equations, particularly concerning the time variable, they yield compr...

We present and analyze a time-fractional, partly diffusive model of two electrically coupled Hindmarsh–Rose neurons in which only the membrane potentials undergo spatial transport, through a nonlinear Neumann m-Laplacian, while the temporal evo...

Precipitation in Mediterranean regions is characterized by strong intermittency and complex organization across multiple temporal scales, posing challenges for understanding its future evolution under climate change. This study examines projected cha...

The existing basic control system of fractional-order modular multilevel converters (FO-MMCs) is mainly designed for ideal operating conditions and exhibits limited adaptability under grid unbalanced conditions. To address this issue, this paper prop...

This study addresses the analysis and numerical solution of a nonlinear time fractional diffusion problem with periodic boundary conditions. A generalized Fourier-based approach is applied to obtain a representation of the solution within a suitable...

The present study is concerned with heteroclinic trajectories of a Caputo fractional-order Lorenz-type model ($0<\alpha \le 1$), a problem that has remained unresolved. Building upon previously known findings, we initially deduce two asymmetric hete...

This paper establishes existence and uniqueness results for a generalized Ćirić–Reich–Rus interpolative contraction involving distinct forward horizons $p,q>1$ and a delay parameter $r>1$. By employing a Matkowski comparison f...

Cyclic high-pressure gas impact is a promising waterless stimulation method for enhancing permeability in deep low-permeability coal seams. However, the nonlinear fracture evolution, cumulative fatigue damage, and coupled fracturing mechanisms during...

The Special Issue “Advances in Boundary Value Problems for Fractional Differential Equations—The Third Edition” continues the successful series of its first two editions and highlights recent developments in the theory and applicati...

This paper presents a Galerkin finite element method based on cubic $\beta$-spline basis functions for the numerical solution of multi-term time-fractional differential equations. The spatial discretization is constructed using a parametric family of...