Fractal and Fractional, Volume 9, Issue 11

This paper introduces two generalized frameworks, the extended bipolar parametric b-metricspace (EBPbMS) and the extended bipolar fuzzy b-metric space (EBFbMS), which unify and extend several existing bipolar and fuzzy metric structures. Within these...

This paper develops a generalized Laplace transform theory within weighted function spaces tailored for the analysis of fractional differential equations involving the $\psi$-Hilfer derivative. We redefine the transform in a weighted setting, establis...

In this paper, we investigate Hermite–Hadamard-type inequalities for harmonically s-convex stochastic processes via Riemann–Liouville fractional integrals. We begin by introducing the notion of harmonically s-convex stochastic processes....

This study investigates the synchronization of coupled fractional-order Markovian reaction-diffusion neural networks (MRDNNs) with partially unknown transition rates. The novelty of this work is mainly reflected in three aspects: First, this study in...

This article explores the temporal dynamics and fractal characteristics of cosmic ray (CR) intensity by conducting a comprehensive analysis of their intrinsic scaling properties. The study utilizes sophisticated methodologies, including standard Detr...

A numerical scheme utilizing shifted Bernstein polynomials is developed to address the variable fractional-order governing equation in viscoelastic fluid-conveying pipes. The pipe’s mechanical response is characterized through a variable fracti...

Traditional linear models struggle to capture the complex behavior of financial markets. This study revisits RMB exchange rate volatility through a nonlinear perspective based on G-expectation and multifractal theory. Using multifractal detrended flu...

This paper investigates the consensus problem in fractional-order multi-agent systems (FOMASs) under Denial of Service (DoS) attacks and actuator faults. A boundary control strategy is proposed, which reduces dependence on internal sensors and actuat...

In dense visual simultaneous localization and mapping VSLAM (VSLAM), a fundamental challenge lies in the inability of existing loss functions to dynamically balance luminance, contrast, and structural fidelity under photometric variations, while thei...

This paper analyzes the Bagley–Torvik fractional-order equation with generalized fractional Hilfer derivatives of two orders for functions in Banach spaces under conditions expressed in the language of weak topology. We develop a comprehensive...

Vector-borne infectious diseases transmitted by vector organisms (e.g., mosquitoes, rodents, and ticks) are recognized as key priorities in global public health. The construction of host–vector interaction frameworks within bipartite networks e...

We present a theoretical examination of the fractional dynamics of information entropy within a semiconductor nanowire system influenced by Rashba spin–orbit interaction and external magnetic fields. Moreover, we determine the fractional nanowi...

This paper presents a novel algorithm for the dynamic analysis of fractional-order viscoelastic spinning disks in the time domain. The novelty mainly lies in the use of the shifted Legendre polynomial algorithm for the direct time-domain numerical an...

The hydro-mechanical coupling in fractures plays a significant role in fluid transport through fracture networks. However, current studies still exhibit certain limitations in the multi-parameter characterization of fracture permeability under stress...

This paper investigates the chaotic and pattern dynamics of the time-fractional Ginzburg–Landau equation. First, we propose a high-precision numerical method that combines finite difference schemes with an improved Grünwald–Letnikov...

Motivated by the strong seasonality of East Asian meteorology and its control on pollution episodes characterized by fluctuation level, we model the season-resolved climatology of the regional PM_2.5 connectivity over the Korean Peninsula. Using daily...

The notion of a system is very old [...]

This paper deals with a new coupled system of integro-differential equations involving the generalized proportional Caputo derivatives equipped with nonlocal four-point boundary conditions. Sufficient criteria for the existence and uniqueness of solu...

In this paper, we evaluate a general class of finite integrals involving the error function, generalized Mittag-Leffler functions, and incomplete Aleph functions. The main result provides a unified framework that extends several known formulas relate...

Gradient accumulation enables training large-scale deep learning models under GPU memory constraints by aggregating gradients across multiple microbatches before parameter updates. Standard gradient accumulation treats all microbatches uniformly thro...

This study models customer patterns using fractal analysis and examines how touchpoints and customer journey mapping shape value to enhance sustainable organizational and customer performance. The analysis is made at cell-level using mathematical mod...

Organic pores serve as crucial storage spaces for shale gas, whose morphology and structure vary significantly among different types of organic matter, directly influencing the storage and seepage capacity of shale gas. The Upper Permian shale in the...

In this paper, we introduce the notion of fuzzy exponential contractions within the framework of fuzzy metric spaces. These mappings, which involve point-dependent exponential terms, are studied under the assumptions of either fuzzy continuity or the...

In the observation of tight sandstone cores, the variations in the hydrocarbon charging usually can be observed in the same geological age reservoirs, which manifest as differential oil staining on the core surface. In order to clarify the micro tota...

We study stochastic variants of the Kairat-II and Kairat-X equations in (3 + 1) dimensions, two canonical models in soliton theory. Random fluctuations are incorporated through a Wiener process, yielding a multiplicative stochastic embedding of the w...

In this paper, we present a collocation algorithm for numerically treating the time-fractional Kuramoto–Sivashinsky equation (TFKSE). Certain orthogonal polynomials, which are expressed as combinations of Chebyshev polynomials, and their shifte...

The nonlocality (capable of associating target dynamics across multiple time moments) and memory properties (able to retain historical trajectories) of fractional calculus serve as the core theoretical approach to resolving the “dynamic informa...

We first investigate the dynamical behavior of an active Brownian particle influenced by a viscoelastic memory effect characterized by a power-law kernel, under the effects of thermal and active noises. We then analyze the dynamics of an active Brown...

Fractional calculus in discrete-time is a recent field that has drawn much interest for dealing with multidisciplinary systems. A result of this tremendous potential, researchers have been using constant and variable-order fractional discrete calculu...

Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the...

Medical image segmentation, driven by the intrinsic fractal characteristics of biological patterns, plays a crucial role in medical image analysis. Recently, universal image segmentation, which aims to build models that generalize robustly to unseen...

The study of economic maps has consistently attracted researchers due to their rich dynamics and practical relevance. A deeper understanding of these systems enables the development of more effective control strategies. In this work, we examine the i...

The current study examines optical soliton solutions in a complicated system of metamaterial-based optical solutions coupled with extremely dispersive couplers. The conformable fractional derivative (CFD) influences the nonlinear refractive index, wh...

Shale gas production dynamics display strong heterogeneity and nonlinearity, posing challenges to conventional analytical methods. This study applies fractal theory to analyze long-term production data from 178 global shale gas fields by calculating...

Focusing on the mining-induced fracture development characteristics of Weakly Cemented Overburden (WCO) in Ultra-Thick Coal Seam (UTCS) extraction, this study, based on the 1101 first mining face in Xinjiang’s Zhundong Coalfield, systematically...

With the widespread application of multi-view data across various domains, multi-view unsupervised feature selection (MUFS) has achieved remarkable progress in both feature selection (FS) and missing-view completion. However, existing MUFS methods ty...

This study presents a comprehensive Lyapunov-based framework for analyzing partial practical stability in nonlinear tempered fractional-order systems (TFOS). We develop novel stability concepts including ${\beta }^{*}$-practical uniform generalized Mittag&n...

Integration in non-integer-dimensional spaces (NIDS) is actively used in quantum field theory, statistical physics, and fractal media physics. The integration over the entire momentum space with non-integer dimensions was first proposed by Wilson in...

This paper examines how the fractional Fourier transform (FrFT) can be used to form and analyze acoustic holograms produced by a moving, linear, frequency-modulated (LFM) source in a shallow water waveguide. In these environments, the source sound fi...

In the present work, we aim to study the inverse problem of recovering an unknown spatial source term in a multi-term time-fractional diffusion equation involving the fractional Laplacian. The forward problem is first analyzed in appropriate fraction...

In this work, we propose a new physics-informed neural network framework based on the method of separation of variables (SVPINN) to solve the distributed-order time-fractional advection–diffusion equation. We develop a new method for calculatin...

The family of stable distributions and, in particular, the $\alpha$-stable distribution increases its applicability in engineering sciences. Examination of industrial data shows that originally assumed Gaussian properties are not so often observed. Re...

Fractional differential equations offer a natural framework for describing systems in which present states are influenced by the past. This work presents a nonlinear Caputo-type fractional differential equation (FDE) with a nonlocal initial condition...

This study presents a novel family of operators, referred to as tempered quantum fractional operators, and investigates the well-posedness of related tempered quantum fractional differential equations. The q-Adams predictor–corrector method is...

We investigate the three-dimensional incompressible fractional Navier–Stokes system with directional fractional diffusion: a vertical dissipative operator of order $2\alpha \in (0,2]$ acting on the full velocity field together with a horizontal...

Hybrid PV-TEG systems can harvest both solar electrical and thermoelectric power, but their operating point drifts with irradiance, temperature gradients, partial shading, and load changes—often yielding multi-peak P-V characteristics. Conventi...

Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of $rq$-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosp...

An integrated analysis including total organic carbon (TOC), X-ray diffraction (XRD), scanning electron microscopy (SEM), and gas adsorption experiments was conducted on core samples from the deep Wufeng–Longmaxi (WF-LMX) Formation in the Zigon...

This paper presents a novel B-spline wavelet-based scheme for solving multi-term time–space variable-order fractional nonlinear diffusion-wave equations. By combining semi-orthogonal B-spline wavelets with a collocation approach and a quasiline...

The significant heterogeneity of continental shale reservoirs within the Permian Lucaogou Formation of the Jimsar Sag presents a major challenge for shale oil exploration. This study aims to quantitatively characterize the pore structure complexity o...