Fractal and Fractional, Volume 9, Issue 3

The primary aim of this manuscript is to establish unique fixed point results for a class of $\Psi$-contraction operators in complete G-metric spaces. By combining and extending various fixed point theorems in the context of $\Psi$-contraction operator...

The compactness, diversity, and nested structures of the old districts in Chinese cities, in terms of their three-dimensional (3D) morphology, are particularly distinctive. However, existing multifractal measurement methods are insufficient in reveal...

In this work, we establish the existence of at least one solution for a p-Laplacian Langevin differential equation involving the $\psi$-Hilfer fractional derivative with antiperiodic boundary conditions. More precisely, we transform the studied proble...

In this paper, we have investigated the existence of normalized solutions for a class of fractional Kirchhoff equations involving nonlinearity and critical nonlinearity. The nonlinearity satisfies $L^2$-supercritical conditions. We transform the problem...

This study presents a shifted Bernstein polynomial-based method for numerically solving the variable fractional order control equation governing a viscoelastic bar. Initially, employing a variable order fractional constitutive relation alongside the...

The accurate description of fracture distributions is a crucial prerequisite for fracturing design and the evaluation of fracturing effects in tight reservoirs. We employed a fractal L-system to establish a tree branch model and derived a planar simu...

Fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shann...

This paper investigates stability switches induced by Hopf bifurcation in a fractional three-neuron network that incorporates both neutral time delay and communication delay, as well as a general structure. Initially, we simplified the characteristic...

This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of...

Mathematics and physics are deeply interconnected. In fact, physics relies on mathematical tools like calculus and differential equations. The aim of this article is to introduce tempered Riemann–Liouville (RL) fractional operators and their pr...

In this paper, we explore the outcomes related to the existence of nonlocal functional boundary value problems associated with pantograph equations utilizing $\psi$-Hilfer fractional derivatives. The nonlinear term relies on unknown functions which co...

This paper consists of an exploration of the wave structures of the Benjamin–Ono equation along with a $\beta$-time fractional derivative. The model concerned is utilized to demonstrate internal waves of deep-stratified fluids. Bright, rational,...

In order to study the failure and fractal characteristics of unloaded rocks, with the help of the true triaxial unloading rock test system and the acoustic emission (AE) monitoring system, rock failure tests were conducted under varying intermediate...

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which i...

Efficient and safe extraction of coalbed methane is essential for reshaping China’s energy composition. This study integrates CO₂ adsorption, N₂ adsorption, and corrected mercury intrusion porosimetry (MIP) data to analyze the full pore size di...

Missing values in time series data present a significant challenge, often degrading the performance of downstream tasks such as classification and forecasting. Traditional approaches address this issue by first imputing the missing values and then in...

In this paper, a second-order predefined-time terminal sliding mode (SPTSM) is proposed, which is investigated for the practical applications of the speed regulation system of a permanent magnet synchronous motor (PMSM) by using predefined-time stabi...

The intent of quantum calculus, briefly q-calculus, is to find q-analogues of mathematical entities so that the original object is achieved when a certain limit is taken. In the case of q-analogue of the ordinary derivative, the limit is $q\to 1^{\&min}$...

This paper proposes a method for searching for pipeline leaks by analyzing the Hurst exponent of acoustic signals. The investigations conducted on the laboratory setup and the current pipelines of the water supply system. During the experiments, thro...

This work introduces the Legendre cardinal functions for the first time. Based on Jacobi and Lobatto grids, two approaches are employed to determine these basis functions. These functions are then utilized within the pseudospectral method to solve th...

This paper examines the self-similarity (long memory) in prices of crude oil markets, namely Brent and West Texas Instruments (WTI), by means of fractals. Specifically, price series are decomposed by stationary wavelet transform (SWT) to obtain their...

In fractal theory, the fractal dimension has been accepted as a quantitative parameter to measure the complexity of fluctuations and the persistence of wind speeds. Typhoons are extreme wind events that damage structures. In this study, on the basis...

The early warning of disasters such as ground pressure in deep hard rock mines has long constrained the safe and efficient development of mining activities. Based on fractal theory and fractal dimension interpretation, this study constructs a microse...

This paper considers a numerical method for solving the stochastic semilinear subdiffusion equation which is driven by integrated fractional Gaussian noise and the Hurst parameter $H\in (1/2,1)$. The finite element method is employed for spatial disc...

Scholars from several disciplines have recently expressed interest in the field of fractional q-calculus based on fractional integrals and derivative operators. This article mathematically applies the fractional q-differential and q-integral operator...

A fractional-order Lorenz system is optimized to maximize its maximum Lyapunov exponent and Kaplan-York dimension using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm. The fractional-order Lorenz system is integrated with a recent...

Rheological complex models of various elastoviscous and viscoelastic fractional-type substances with polarized piezoelectric properties are of interest due to the widespread use of viscoelastic–plastic bodies under loading. The word “over...

Efficient coordination of directional overcurrent relays (DOCRs) is vital for maintaining the stability and reliability of electrical power systems (EPSs). The task of optimizing DOCR coordination in complex power networks is modeled as an optimizati...

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face c...

This paper is dedicated to investigating a highly accurate numerical solution for a class of 2D nonlinear time-dependent partial integro-differential equations with multi-term fractional integral items. These integrals are weakly singular with respec...

This paper presents a generalized fractional Stockwell transform (GFST), extending the classical Stockwell transform and fractional Stockwell transform, which are widely used tools in time–frequency analysis. The GFST on $L^2(\mathbb{R},\mathbb{C})$ is defined as a...

Granular samples are often used to characterize the pore structure of shale. To systematically analyze the influence of particle size on pore characteristics, case studies were performed on two groups of organic-rich deep shale samples. Multiple meth...

In this manuscript, we introduce the concept of fuzzy S-metric spaces and study some of their characteristics. We prove a fixed-point theorem for a self-mapping on a complete fuzzy S-metric space. To illustrate the versatility of our new ideas and re...

In the current context of the global energy landscape, China is facing a growing challenge in oil and gas exploration and development. It is difficult to evaluate the log data because of the lithological composition of igneous rocks, which displays a...

This study investigated market efficiency across 20 major commodity assets, including crude oil, utilizing fractal analysis. Additionally, a rolling window approach was employed to capture the time-varying nature of efficiency in these markets. A Gra...

This paper introduces a novel model-free fractional-order composite control methodology specifically designed for precision positioning in permanent magnet synchronous motor (PMSM) drives. The proposed framework ingeniously combines a composite contr...

This work presents a fractional order Proportional Integral and Derivative controller with adaptation characteristics in the control parameters depending on the required output, gain scheduling fractional order PID (GS-FO-PID). The fractional order P...

This paper investigates the fracture surfaces and fracture performance of recycled aggregate concrete (RAC) using fringe projection technology. This non-contact, point-by-point, and full-field scanning technique allows precise measurement of RAC&rsqu...

The purpose of this paper is to propose a fractal–fractional-order for computer virus propagation dynamics, in accordance with the Atangana–Baleanu operator. We examine the existence of solutions, as well as the Hyers–Ulam stability, uniqueness, non-...

Multi-focus image fusion is an important method for obtaining fully focused information. In this paper, a novel multi-focus image fusion method based on fractal dimension (FD) and parameter adaptive unit-linking dual-channel pulse-coupled neural netw...

As the frequency of disasters increases worldwide, it has become increasingly important to raise awareness of the risks and mitigate their effects through effective disaster management. Anticipating disaster risks and ensuring timely evacuations are...

In this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order $\alpha \in (1,2)$. The novel compact difference-Galerkin spectral method ca...

This manuscript studies the M-fractional Landau–Ginzburg–Higgs (M-fLGH) equation in comprehending superconductivity and drift cyclotron waves in radially inhomogeneous plasmas, especially for coherent ion cyclotron wave propagation, aimin...

The accurate and efficient simulation of seismic wave energy dissipation and phase dispersion during propagation in subsurface media due to inelastic attenuation is critical for the hydrocarbon-bearing distinction and improving the quality of seismic...

This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries...

A continuous adaptive stabilization technique for the unstable period-1 orbit of the fractional difference logistic map is presented in this paper. An impulse-based control technique without short oscillatory transients right after the control impuls...

For the non-homogeneous fractional-order Hammerstein multiple input single output (MISO) system, a method for identifying system coefficients and fractional-order parameters in stages is proposed. The coefficients of the system include the coefficien...

This study investigates the complex dynamics and control mechanisms of fractional-order glucose–insulin regulatory systems, incorporating memory-dependent properties through fractional derivatives. Employing the Laplace–Adomian Decomposition Method (...

Accurate identification of growth and development stages is critical for orthodontic diagnosis, treatment planning, and post-treatment retention. While hand–wrist radiographs are the traditional gold standard, the associated radiation exposure...

A new predefined time sliding mode control theme is proposed and applies to the multi-switch combination–combination synchronization (MSCCS) of fractional-order (FO) hyperchaotic systems. Firstly, based on the Lyapunov stability theory, we demo...