Fractal and Fractional, Volume 9, Issue 6

A clear method is provided to explain a new approach for solving systems of fractional Navier–Stokes equations (SFNSEs) using initial conditions (ICs) that rely on the Elzaki transform (ET). A few steps show the technique’s validity and u...

In this paper, we investigate a class of fuzzy partially differentiable models for Caputo–Hadamard-type Goursat problems with generalized Hukuhara difference, which have been widely recognized as having a significant role in simulating and anal...

A Bayesian network (BN) is an uncertainty processing model that simulates human cognitive thinking on the basis of probability theory and graph theory. Its network topology is a directed acyclic graph (DAG) that can be manually constructed through ex...

Since polynomial regression models are generally quite reliable for data that can be handled using a linear system, it is important to note that in some cases, they may suffer from overfitting during the training phase. This can lead to negative valu...

Evolution equations with fractional-time derivatives and singular memory kernels are used for modeling phenomena exhibiting hereditary properties, as they effectively incorporate memory effects into their formulation. Time-fractional partial integro-...

This study is organized to introduce the concept of center–radius $\left(cr\right)$-ordered fuzzy number-valued convex mappings. Based on this class of mappings, we have initiated the idea of fuzzy number-valued extended $cr$-ℏ convex mappings incorpora...

The time-fractional generalized Burger–Fisher equation (TF-GBFE) is utilized in many physical applications and applied sciences, including nonlinear phenomena in plasma physics, gas dynamics, ocean engineering, fluid mechanics, and the simulati...

This research proposes a fractional-order adaptive neural control scheme using an optimized backstepping (OB) approach to address strict-feedback nonlinear systems with uncertain control directions and predefined performance requirements. The OB fram...

The complementary dual of entropy has received significant attention in the literature. Due to the emergence of many generalizations and extensions of entropy, the need to generalize the complementary dual of uncertainty arose. This article develops...

This study enhances the classical deterministic SIR model by incorporating soliton-like dynamics and gradient-induced diffusion, effectively capturing the complex spatiotemporal patterns of disease transmission within nomadic populations. The propose...

The acidification modification treatment of coal is a key technical means to improve the permeability of coal seams and enhance the efficiency of coalbed methane extraction. Yet, current acidic fracturing fluids are highly corrosive, corroding downho...

The Hurst phenomenon is regarded as an intrinsic characteristic of many natural processes closely related to high uncertainty and long-term persistence. Temperature and precipitation are the two important meteorological factors characterizing the cli...

In this paper, we apply Grünwald–Letnikov-type fractional-order calculus to simulate the growth of Serbia’s gross domestic product (GDP). We also compare the fractional-order model’s results with those of a similar integer-orde...

This study investigates the magnetic fields produced by a three-solenoid system configuration using both traditional numerical solvers and fractional integral methods. We focus on the role of mesh resolution in influencing simulation accuracy, examin...

In this study, we analyze a time-fractional spatiotemporal $SIR$ model in a specific area $\Omega$. Taking into account the available resources, vaccines are allocated to region ${\omega }_1\subseteq \Omega$ and treatments to region ${\omega }_2\subseteq \Omega$, which...

The deformation control of surrounding rock in the combustion air zone is crucial for the safety and efficiency of underground coal gasification (UCG) projects. Coal-bearing sandstone, a common surrounding rock in UCG chambers, features a brittle str...

In this study, we define the $k$-Cullen, $k$-Cullen–Lucas, and Modified $k$-Cullen sequences, and certain terms in these sequences are given. Then, we obtain the Binet formulas, generating functions, summation formulas, etc. In addition, we examine t...

This paper investigates the synchronization control problem for delayed fractional-order neural networks (DFONNs) with mismatched parameters. A novel synchronization behavior termed quasi-Mittag-Leffler projective synchronization (QMLPS) is studied....

This paper addresses the existence of solutions to a Hadamard fractional differential equation of arbitrary order on an infinite interval, subject to integral boundary conditions that incorporate both Riemann–Stieltjes integrals and Hadamard fr...

The present work proposes a novel fractional-order multifunction filter topology in current-mode (CM), which is designed based on the Modified Current Feedback Operational Amplifier (MCFOA). The proposed design simultaneously generates fractional-ord...

Repeated mining under insufficiently collapsed gobs is a complex process in underground mining and is associated with safety hazards such as ground collapse and subsidence. The effect of layer spacing on the fracture network evolution and fluid trans...

This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerfu...

The study of fractional differential equations is gaining increasing significance due to their wide-ranging applications across various fields. Different methods, including fixed-point theory, variational approaches, and the lower and upper solutions...

This study introduces an innovative analytical solution to the time-fractional Cattaneo heat conduction equation, which models photothermal transport in metallic thin films subjected to short laser pulse irradiation. The model integrates the Caputo f...

Sandstone reservoirs exhibit strong heterogeneity and complex microscopic pore structures, presenting challenges for quantitative characterization. This study investigates the Chang 8 tight sandstone reservoir in the Jiyuan, Ordos Basin through analy...

This paper constructs a fundamental mathematical model to depict the therapeutic effects of two drugs on breast cancer patients. The model is described by fractional order differential equations with two control variables. Two scenarios are considere...

In this research, we consider the inverse problem for the wave equation under an unknown initial condition. A generalized solution to the direct problem was formulated, its correctness was established, and the stability assessment was obtained. The i...

Chaotic behavior and memory-dependent dynamics in fractional-order brushless DC motors (FOBLDCMs) pose significant challenges for robust and stable control design, particularly when physical constraints such as actuator saturation and rate limitation...

This paper proposes a weak Galerkin (WG) finite element method for solving a multi-dimensional evolution equation with a weakly singular kernel. The temporal discretization employs the backward Euler scheme, while the fractional integral term is appr...

This study investigates the coupled effects of waste rock-to-tailings ratio (WTR) and curing temperature on the pore structure and mechanical performance of cemented tailings waste rock backfill (CTRB). Four WTRs (6:4, 7:3, 8:2, 9:1) and curing tempe...

In this article, we introduce and study a novel class of polynomial $\phi$-contractions, which simultaneously generalizes classical polynomial contractions and $\phi$-contractions within a unified framework. We establish generalized fixed point theorem...

This paper deals not only with pointwise and uniform convergence but also Y-valued fractional approximation results by univariate symmetrized neural network (SNN) operators on Banach space $\left(Y,∥.∥\right)$. Moreover, our main motivation in this work is to compare...

Fractal theory of particle size distribution (PSD) is a widely used approach in soil science. However, fractal studies on sandstone PSDs are scarce in sedimentology and geology. Taking littoral sandstones in the Carboniferous Donghetang Formation of...

In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equatio...

In this paper, we are studying a class of nonlinear fractional difference equations with time-varying delays in Banach space. By means of mathematical induction and the Picard iteration method, we first obtain the existence result of this fractional...

This study combines artificial intelligence (AI) with mathematical modeling to improve the forecasting of the water cycle mechanism. The proposed model simulates the development of global temperature, precipitation, and water availability, integratin...

In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For...

This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag...

Campylobacteriosis has been described as an ever-changing disease and health issue that is rather dangerous for different population groups all over the globe. The World Health Organization (WHO) reports that 33 million years of healthy living are lo...

This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing $t^{\mathsf{\alpha }}$ with $\mathsf{\tau }$. It demonstrates the potential to capture the influence of the fractal parameter on the system’s damping frequen...

In this study, we develop a fractional-order mathematical model for investigating the transmission dynamics of monkeypox (Mpox), accounting for interactions between humans, rodents, and environmental reservoirs. The model uniquely integrates two key...

Renewable energy sources (RESs) are increasingly combined into the power system due to market liberalization and environmental and economic benefits, but their weather-dependent variability causes power production and demand mismatches, leading to is...

Various sectors focus on transitioning to clean and renewable energy sources, particularly airport microgrids (AMGs), which offer the potential for highly reliable and resilient operations. As airports increasingly integrate renewable energy sources,...

In this paper, we investigated fractal cluster structures of colloidal particles in tin dioxide films obtained from lyophilic film-forming systems SnCl₄/EtOH/NH₄OH with different pH levels. It was revealed that at the ratio Sn > Cl₂ > O₂, N₂ =...

This article presents a comprehensive study of the (2+1)-dimensional Zakharov–Kuznetsov (ZK) $(q,p,r)$ equation with time fractional derivativeUtilizing the fractional Lie group method, we derive several results, including the symmetries, similar...

The heterogeneity of shale pore systems, which is controlled by thermal maturation, fundamentally governs hydrocarbon storage and migration. Artificial sequence maturity samples of Xiamaling shale were obtained through a temperature–pressure si...

This study examines the price dynamics of the UK Emission Trading Scheme (UK ETS) by integrating advanced computational methods, including deep learning and statistical modelling, to analyze and simulate carbon market behaviour. By analyzing long-mem...

In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant ($\mathsf{\Lambda }$), and an ad-hoc...

This paper concludes a few fixed-point outcomes involving almost Matkowski contraction-inequality of Pant type in a relational metric space. The findings established here enhance, expand, consolidate and develop several noted outcomes. In order to ar...

Time-fractional convection–diffusion equations are significant for their ability to model complex transport phenomena that deviate from classical behavior, with numerous applications in anomalous diffusion, memory effects, and nonlocality. This...