Fractal and Fractional, Volume 10, Issue 4

Liquid nitrogen (LN₂) fracturing is a highly promising stimulation technology for unconventional reservoirs. Understanding its in situ fracture network formation mechanism is essential for engineering practice. This study investigates coal rock fract...

An integrated analysis incorporating total organic carbon (TOC) content measurement, X-ray diffraction (XRD), scanning electron microscopy (SEM), and gas adsorption experiments was performed on core samples from Well FY1-4 of the upper-fourth Shaheji...

This paper proposes and studies a new class of nonlinear nonlocal problem driven by a tempered Caputo-type fractional derivative with respect to an arbitrary smooth kernel. The novelty lies in treating a single nonlocal integro-delay setting that sim...

Subdiffusion on graphs is often modeled by time-fractional diffusion equations; yet, its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random time change...

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five ep...

The development of More Electric Aircraft (MEA) necessitates that Electro-Hydrostatic Actuator (EHA) controllers achieve exceptional power density within rigorously constrained volumes. However, the compact layout design of these controllers constitu...

This research paper demonstrates how to manage Caputo fractional neutral integro-differential equations which include both integral and nonlinear elements through a unified framework that models dynamic systems with memory-based dynamics. The researc...

A method for analyzing long-term (1997–2025) continuous records of low-frequency global seismic noise measured at a network of 229 broadband seismic stations distributed across the Earth’s surface is proposed in this study. The method is...

This paper develops novel similarity and dissimilarity measures for $(p,q,r)$-fractional fuzzy sets to enhance information discrimination and decision-making under complex uncertainty. We first introduce axiomatic dissimilarity measures and establish t...

The harmonic equivalent method is a non-perturbative approach to nonlinear vibration issues, aiming to create linearly coupled systems from coupled vibrations. However, there is still much to be discovered about managing interconnected nonlinear comp...

In this paper, we introduce, for the first time, a novel class of (center-radius order $(P,\mathrm{m})$-superquadratic interval-valued functions) $\mathfrak{cr}$-$(P,\mathrm{m})$-superquadratic $\mathcal{IVF}$s, and systematically investigate their fundamental structural properties. Building upon...

We prove the existence of a positive ground state solution for a fractional $(p,q)$-Laplacian Choquard equation that features both a singularity and an upper critical exponent. The proof relies on a combination of the Nehari manifold technique and Ekel...

This paper presents a unified theoretical and numerical investigation of Hilfer-type fuzzy fractional control systems with infinite continuous delay. By employing contraction mapping principles and compact semigroup theory, we establish rigorous solv...

The purpose of this research work is to propose and develop the notion of $\left(\alpha ,\psi \right)$-contractions in the setting of extended $\mathcal{F}$-metric spaces and to establish corresponding fixed point results. Using these results, we derive fixed point results for...

This work develops a fuzzy piecewise fractional derivative (FPFD) model for cancer-immune-angiogenesis dynamics under uncertainty. Five fuzzy state variables track tumor cells, immune effectors, vessel density, oxygen, and drug concentration. We empl...

Pore structure and multifractal characteristics are two critical indicators for evaluating the heterogeneity of tight sandstone reservoirs. An integrated analysis comprising physical property tests, X-ray diffraction, casting thin sections, scanning...

In this research article, we introduce and develop the notion of complex-valued b-suprametric spaces as a natural generalization of existing metric-type structures. Fundamental concepts, including convergence, Cauchy sequences, and completeness, are...

Understanding the evolution of coal pore–fracture structures under coupled stress paths and creep deformation is critical for enhancing coalbed methane extraction and preventing coal and gas outbursts. In this study, coal samples from the Ningt...

In this paper, we investigate a $(k,{\rm Y})$ fractional quadratic integral equation in the Banach space of real-valued continuous functions on $[0,1]$. By using a measure of noncompactness associated with monotonicity and Darbo’s fixed point the...

In this article, we present a new approximate solution for blood nanofluid having gold nanoparticles as it flows near a stretching porous cylinder in fractal space. A Casson non-Newtonian magneto-bio-nanofluid flowing through a porous medium is consi...

Pneumatic transmission lines play a critical role in the dynamic performance of soft robotic actuation systems, yet their behaviour is difficult to capture using conventional integer-order (IO) models. In long, slender pipelines, compressibility, vis...

In this research work, we investigate a nonlinear fractional initial value problem involving the Atangana-Baleanu-Caputo derivative of order $0<\alpha <1.$ By means of the associated fractional integral operator, the problem is converted into an...

This article focuses on the fixed-time synchronization problem for fractional-order fuzzy cellular neural networks (FOFCNNs) with information interactions and time-varying delays. To capture the complex dynamics of practical networks, nonlinear activ...

Coalbed methane is vital for the transition toward low-carbon energy systems, yet its recovery efficiency is critically limited by inaccurate classification of movable water during drainage and depressurization due to the complex pore–fracture...

Moderate thermal exposure can significantly influence the mechanical behavior of volcanic rocks by inducing microcrack development and altering crack network characteristics. However, quantifying such damage processes remains challenging when relying...

This paper investigates non-fractional operators, a type of nonlocal operator, within the framework of Orlicz spaces. Using inclusions between certain function spaces, we prove the continuity and/or compactness of generalized operators in Orlicz spac...

In recent years, fractional HIV models have received increasing attention. This study derives a fractional HIV model using the continuous-time random walk (CTRW) method, endowing the mathematical model with physical significance. Based on the transmi...

Accuracy in fractional numerical integration is often limited by the regularity of the integrand. This work proposes a flexible error estimation framework for proportional Caputo-hybrid integral operators based on $\mathfrak{s}$-convexity. We introduce a parametr...

This study proposes an improved retinal blood vessel segmentation method to enhance the diagnosis of microvascular retinal complications. The proposed method extracts local shape features from retinal images utilizing a fractional Hessian matrix, whi...

This study offers a computational framework that analyzes the escape characteristics of transcendental complex maps by utilizing the AK iteration scheme. The well-known polynomial map of the form $z^n+c$ is generalized to the form $z^n+\sin \left(z\right)+\log \left(c^m\right)$, wit...

This study uses a fractional operator technique to analyze a novel class of special polynomials. These polynomials are designated as fractional Gould–Hopper–Bell–Apostol-type polynomials. We first define the operational expression o...

This paper presents an intelligent fault identification approach integrating composite multiscale fractional fuzzy diversity entropy (CMFFDE) for feature extraction, joint mutual information (JMI) for feature selection, and an extreme learning machin...

This paper introduces a comprehensive class of multiparameter post-quantum fractional quadrature inequalities, unifying classical error bounds within the setting of the post-quantum Riemann–Liouville fractional integral. By incorporating multip...

This paper investigates the finite time stability (FTS) of multi-delayed systems with Riemann-Liouville fractional order (RLFO). Firstly, a lemma on the FTS criterion is established for RLFO multi-delay systems, which lays the theoretical groundwork...

This study investigates, at a microscale, urban sensible heat flux and Kolmogorov entropy in locations with varying degrees of urban densification according to regular geometries, and examines their effect on fractal dimension. To this end, an ultras...

Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in en...

Thermal regulation using Peltier cells presents challenges due to high inertia, memory effects, and energy constraints in embedded systems. This paper introduces the FOPID with Adaptive Supervisor (FOPID-AS) scheme, combining a PSO-optimized fraction...

In this paper, we investigate the well-posedness and stability of a class of coupled systems of deformable fractional differential equations in Banach spaces. The deformable fractional derivative, which interpolates continuously between a function an...

In this investigation, the nonlinear dust-acoustic waves in the lunar terminator region are studied in a three-component complex plasma comprising Boltzmann-distributed electrons and ions and inertial, cold, negatively charged dust grains. The fluid...

The dominant pores governing methane adsorption in coal are micropores (pore size < 2 nm). Their spatial heterogeneity can be quantitatively characterized using multifractal theory; however, the evolution patterns and mechanisms of microporous str...

Fractional calculus and distribution theory share a common conceptual origin in the symbolic interpretation of differentiation and integration. Despite this connection, most developments in fractional calculus have traditionally been formulated withi...

The motivation for this paper is that most of the works on secondary frequency control are focused on conventional synchronous communication approaches. To extend this research, this paper investigates the sampled-data-based $H_{\infty }$ load frequency c...

In this paper, we study the existence of normalized solutions for anisotropic nonlinear Schrödinger equation with potentials which are bounded and converge to positive constants at infinity. In the mass subcritical case, we show the energy funct...

The double natural generalized Laplace transform decomposition method (DNGLTDM) is proposed as a new approach for solving singular linear and non-linear two-dimensional Boussinesq equations involving fractional partial derivatives. This method combin...

In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional Kirchhoff–Schrödinger problem with logarithmic nonlinearity. By combining the Pohozaev identity, the penalization technique, and the c...

In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends...

In this study, we introduce new versions of fuzzy fractional integral operators for both one- and two-variable cases. Using these operators, several Hermite–Hadamard-type ($H$-type) inclusions are established for fuzzy-number-valued convex functi...

Forecasting financial time series (FTS) is essential for analyzing and understanding the dynamics of financial markets. Traditional recurrent neural network (RNN) models often suffer from low prediction accuracy on non-stationary and abruptly changin...

Differential equations with fractional order play an important role in modeling some natural phenomena. This paper investigates the dynamics of the fractional-order commensal symbiosis model with the Allee effect. This model describes the relationshi...

In this paper, we revisit the recent result of Luo, Xu, and Raina on an Erdélyi-type integral for Saran’s three-variable hypergeometric function $F_K$. We provide a new proof of this integral and derive an attractive new integral related to...