Fractal and Fractional, Volume 8, Issue 4

Thin sections, AIM-SEM, MICP, and nitrogen adsorption were performed on laminated and layered shales to characterize their complex pore and fracture structure. Combining the MICP model with the FHH model, this work proposes a new fractal method for l...

In this paper, a cascade control structure is suggested to control servo systems that normally include a servo motor in coupling with two kinds of mechanism elements, a translational or rotational movement. These kinds of systems have high demands fo...

The aim of this research is to introduce two new notions, $\mathsf{\Theta }$-($\mathsf{\Xi }$,h)-contraction and rational ($\alpha$,$\eta )$-$\psi$-interpolative contraction, in the setting of $\mathfrak{F}$-metric space and to establish corresponding fixed point theorems. To reinforce un...

This study investigated the influence of movable oil on the pore structure of various shale types, analyzing 19 shale samples from Well X in the Mahu Sag of the Junggar Basin. Initially, X-ray diffraction (XRD) analysis classified the shale samples....

Studying atmospheric temperature characteristics is crucial under climate change, as it helps us to understand the changing patterns in temperature that have significant implications for the environment, ecosystems, and human well-being. This study p...

In order to explore the influence of dip angles on the deformation and failure of a coal–rock combination, uniaxial compression experiments were carried out on a coal–rock combination with different dip angles, and the acoustic emissions...

In this study, we investigate multiscale auto- and cross-correlation structural characteristics of sea surface temperature (SST) variability using our new methodology, called the multifractal asymmetric cross-correlation analysis (MF-ACCA), incorpora...

Here, we investigate the spectral and oscillation theory for a class of fractional differential equations subject to specific boundary conditions. By transforming the problem into a modified version with a classical structure, we establish the orthog...

COVID-19 is a lung disease caused by a coronavirus family virus. Due to its extraordinary prevalence and associated death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of rel...

Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on t...

This work investigates the solvability of the generalized Hilfer fractional inclusion associated with the solution set of a controlled system of minty type–fuzzy mixed quasi-hemivariational inequality (FMQHI). We explore the assumed inclusion v...

This paper introduces an analog integrated fractional order type-2 fuzzy PID control system. Current approaches frequently depend on energy-intensive embedded digital systems, consuming substantial energy levels ranging from a few μW to mW. To add...

Fractional calculus has had a powerful impact on recent research, with many applications in different branches of science and engineering [...]

In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through s...

This paper applies fractional calculus to a practical example in fluid mechanics, illustrating its impact beyond traditional integer order calculus. We focus on the classic problem of a rigid body rotating within a uniformly rotating container, which...

This work investigates novel fractional Hadamard integral inequalities by utilizing extended convex functions and generalized Riemann-Liouville operators. By carefully using extended integral formulations, we not only find novel inequalities but also...

The degree of irregularity and complexity of the pore structure are comprehensively reflected in the fractal dimension. The porosity of coal was determined by its fractal dimension, where a larger dimension indicates a lower porosity. Fractal theory...

In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzH...

This research article introduces the four-dimensional natural transform Adomian decomposition method (FNADM) for solving the (3+1)-dimensional time-singular fractional coupled Burgers’ equation, along with its associated initial conditions. The...

Silicon neurons are bioinspired circuits with the capability to reproduce the modulation through pulse-frequency observed in real neurons. They are of particular interest in closed-loop schemes to encode the control signal into pulses. This paper pro...

This research utilizes the innovative fractional-order Archimedean spiral moth–flame optimization (FO-AMFO) technique to address the issues of the optimal reactive power dispatch (ORPD) problem. The formulated fitness function aims to minimize...

AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifracta...

This work introduces an alternative approach for developing a customized Metaheuristic (MH) tailored for tuning a Fractional-Order Proportional-Integral-Derivative (FOPID) controller within an Automatic Voltage Regulator (AVR) system. Leveraging an A...

The Zoomeron equation plays a significant role in many fields of physics, especially in soliton theory, such as helping to reveal new distinctive properties in different physical phenomena such as fluid dynamics, laser physics, and nonlinear optics....

This study investigates the dynamics of predator–prey interactions with non-overlapping generations under the influence of fear effects, a crucial factor in ecological research. We propose a novel discrete-time model that addresses limitations...

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo’s frac...

We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the ex...

Desiree R. Azizoddin PsyD from the TSET Health Promotion Research Center, Stephenson Cancer Center at the University of Oklahoma Health Sciences Center, USA, was not included as an author in the original publication [...]

International students play a crucial role in China’s talent development strategy. Thus, predicting overseas talent mobility is essential for formulating scientifically reasonable talent introduction policies, optimizing talent cultivation syst...

Over the past few years, many scholars began to study averaging principles for fractional stochastic differential equations since they can provide an approximate analytical method to reduce such systems. However, in the most previous studies, there i...

The precursor of rock failure around a hole has always been one of the research hotspots in the field of rock mechanics, and the distribution of the plastic zone is often adopted to reflect the location and form of rock failure. The shape of the plas...

This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample...

In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines...

This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of t...

This paper deals with a nonlocal fractional coupled system of $(k,\psi )$-Hilfer fractional differential equations, which involve, in boundary conditions, $(k,\psi )$-Hilfer fractional derivatives and $(k,\psi )$-Riemann–Liouville fractional integral...

Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are th...

Fractal geometry is a geometry that focuses on irregular geometric forms and can quantitatively describe rough and uneven surfaces and interfaces. As the main material for making natural fiber geotextile, rice straw fiber can reduce the direct impact...

Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a dif...

This work presents a quantitative analysis of the transmission dynamics of dengue using the Caputo–Fabrizio fractional-order derivative. It presents an extensive framework for modeling a dengue epidemic, including the various stages of infectio...

In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz...

The fractal properties of carbon paste electrodes (CPEs) and carbon paste electrodes modified with ionic liquid (IL), AuTiO₂/graphene oxide, and IL/AuTiO₂/graphene oxide were investigated using scanning electron microscopy (SEM), and cyclic voltammet...

This paper is devoted to the research of the isomorphic multidimensional cyclic structure and multidimensional phase structure of the cyclic random process (CRP) and to its formation method, which enables a rigorous formalization of intuitive ideas c...

The measurements, recorded as time series (TS), of urban meteorology, including temperature (T), relative humidity (RH), wind speed (WS), and pollutants (PM₁₀, PM_2.5, and CO), in three different geographical morphologies (basin, mountain range, and c...

This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead...

The primary goal of this research is to offer an efficient approach to solve a certain type of fractional integro-differential and differential systems. In the Caputo meaning, the fractional derivative is examined. This system is essential for many s...

This study delves into the convergence of operators and the viscoelastic properties of fractal ladder and tree structures. It proves the convergence of fractal stiffness operators through operator algebra, revealing a fundamental connection between o...

In this study, we present a novel approach for the numerical solution of high-order ODEs and MTVOFDEs with BCs. Our method leverages a class of GSJPs that possess the crucial property of satisfying the given BCs. By establishing OMs for both the ODs...

Most geophysical and geochemical data are commonly acknowledged to exhibit fractal and multifractal properties, but the fractal characteristics of polarizability have received limited attention from the literature. The present study demonstrates that...

There is an increasing interest in determining if there exist observable patterns or structures within the digits of irrational numbers. We extend this search by investigating the interval in position between two consecutive occurrences of the same d...

This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a...