2025 December - 76 articles
Semi-supervised learning (SSL) is critical for medical image segmentation but often struggles with network dependency and pseudo-label error accumulation. To address these issues, we propose a fractal-dimension-guided hierarchical contrastive learnin...
Short-duration extreme rainfall is a major trigger of flash floods and urban inundation, yet its quantification remains a profound challenge due to the scarcity of high-resolution observations. This review synthesizes how three central paradigms of n...
Theaim of this research is to establish existence and uniqueness results for the Riemann–Liouville fractional integral equation of order
This paper proposes a novel fractional-order African vulture optimization algorithm (FO-AVOA) for solving the optimal reactive power dispatch (ORPD) problem. By integrating fractional calculus into the conventional AVOA framework, the proposed method...
This paper investigates the synchronization problem of fractional-order coupled neural networks (FOCNNs) featuring higher-order interactions and mixed delays under an event-dependent intermittent control framework. The proposed model incorporates hig...
This paper develops a unified synchronization framework for octonion-valued fractional-order neural networks (FOOVNNs) subject to mixed delays, Lévy disturbances, and topology switching. A fractional sliding surface is constructed by combining...
Fractional-order chaotic systems describe complex dynamic processes with memory effects and long-range correlations, while integer-order chaotic systems are generally viewed as a special case of fractional-order counterparts. This close relationship...
Understanding the temporal dynamics of urban air pollution is essential for effective environmental management, yet the nonlinear and scale-dependent behavior of key pollutants remains insufficiently explored. This study examines the multifractal pro...
This study presents a fractional-order dynamical model for diabetes progression, formulated by extending an existing obesity model using the Atangana–Baleanu fractional derivative, termed the Atangana–Baleanu Fractional Diabetes Model (AB...
This study proposes an automatic denatured recognition method of biological tissue during high-intensity focused ultrasound (HIFU) therapy. The technique integrates ultrasonic phase space reconstruction (PSR) with a convolutional block attention mech...
The present study explores bone healing patterns induced by orthodontic (OE) and surgical extrusion (SE) of structurally compromised teeth, where extrusion techniques are commonly used in rehabilitation. Changes in the trabecular bone were assessed b...
The pore complexity and heterogeneity in porous media display obvious fractal characteristics, which can be characterized by the fractal dimension for the pore tortuosity (DT) and the fractal dimension for the pore size (Df). Correspondingly, a three...
Difference schemes for the numerical solution of fractional differential equations rely on discretizations of the fractional derivative. In this paper, we obtain the second-order expansion formula for the L1 approximation of the Caputo fractional der...
This study presents an efficient numerical scheme for solving the generalized nonlinear time-fractional Klein–Gordon equation. The Caputo time-fractional derivative is discretized using a conventional finite-difference approach, while the spati...
The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the...
In this manuscript, we investigate a fractional-order conformable three-dimensional chaotic financial model with interest rate, investment demand, and price index compartments. On the application of fixed-point theorems and nonlinear analysis, we est...
In this work, we propose a simple analytical/semi-analytical approach to solve various φ,ψ-fractional partial differential equations (φ,ψ-FPDEs) using initial and boundary conditions (ICs, BCs) depending on the φ,ψ-Double Elza...
A modified Enzyme Action Optimizer (mEAO) is proposed to tune a Fractional-Order Proportional–Integral–Derivative (FOPID) controller for precise temperature regulation of a nonlinear continuous stirred tank reactor (CSTR). The nonlinear r...
The fractal extension of the time-dependent Ginzburg–Landau (TDGL) equation, formulated within the framework of Scale Relativity, generalizes superconducting dynamics to non-differentiable space–time. Although analytically well establishe...
This research employs a Caputo fractional-derivative model to investigate the effects of magnetic field inclination and thermal radiation on the unsteady flow of a Casson fluid over an inclined plate in a porous medium. The model incorporates memory...
We extend the classical fractal uncertainty principle (FUP) framework in time-frequency analysis by exploring several novel directions. First, we generalize the FUP beyond the classical Gaussian window by investigating non-Gaussian windows and the co...
Researchers have devised numerous methods to model intricate behaviors in phenomena that unfold in multiple stages. This work focuses on a specific category of piecewise hybrid terminal systems characterized by delay. To account for hereditary memory...
This study employs the modified extended direct algebraic method (MEDAM) to investigate the generalized nonlinear fractional
This work focuses on the finite-time synchronization control (FTSC) for fractional-order chaotic systems (FOCSs) subject to uncertain dynamics, unknown parameters and input nonlinearities. In the control law design, the uncertain dynamics of the FOCS...
In this paper, we consider the family of parameterized Mandelbrot-like sets generated as any point
In this paper, we study the local stability of an incommensurate fractional reaction–diffusion glycolysis model. The glycolysis process, fundamental to cellular metabolism, exhibits complex dynamical behaviors when formulated as a nonlinear rea...
Extracting high-quality surface wave dispersion curves from crosscorrelation functions (CCFs) of ambient noise data is critical for seismic velocity inversion and subsurface structure interpretation. However, the non-uniform spatial distribution of n...
This study presents a novel softsign-function-based fractional-order proportional–integral–derivative (softsign-FOPID) controller optimized using the fungal growth optimizer (FGO) for the stabilization and precise position control of an u...
Many problems in classical and quantum physics, statistical physics, engineering, biology, psychology, economics, and finance are inherently global rather than merely local, often exhibiting long-range correlations in time and space, memory effects,...
Pore–throat structure and gas distribution are critical factors in evaluating the quality of tight sandstone reservoirs and hydrocarbon resource potential. Twelve tight sandstone samples from the Lower Permian Shihezi Formation in Hangjin Banne...
This paper investigates the fixed-time synchronization of fractional-order proportional delay Hopfield neural networks (PDHNNs) with bounded parameter uncertainties. Unlike constant delay and bounded variable delay, proportional delay has time-varyin...
In this study, a time-fractional extension of the classical Theis problem with an exponential source term is investigated in a confined aquifer. The governing equation is modeled using two different fractional derivatives—the Caputo and Atangan...
In this article, mathematical modeling and stability analysis of Lyme disease and its transmission dynamics using Caputo fractional-order derivatives is presented. The compartmental model has been formulated to analyze the spread of Borrelia burgdorf...
The Upper Permian marine shale of the inter-platform basin in the Nanpanjiang Basin are rich in organic matter, widely distributed, and relatively thick, indicating abundant resource potential for hydrocarbon exploration. To clarify the sedimentary c...
In recent decades, the fractional derivative (FD) and memory-dependent derivative (MDD) have been borrowed for modifying the unsteady diffusion process. Yet, according to their definitions, only memory effects in temporal sense are reflected. To make...
Amid growing threats of image data leakage and misuse, image encryption has become a critical safeguard for protecting visual information. However, many recent image encryption algorithms remain constrained by trade-offs between security, efficiency,...
We study the multifractal structure of irregular sets arising from Fibonacci-weighted sums of sequences of random variables. Focusing on Cantor-type subsets
This paper proposes a new simple method for generating fractal-like aggregates in 2D real spaces. The idea is to use an initial fractal aggregate and simulate a Gravity-based attraction from a distant point (using a gravity attractor with a large mas...
The method of deriving fractional-order differential equations using Riesz fractional-order calculus is a new breakthrough, and it is possible to use the inverse scattering transform (IST) to solve the analytical solutions of the derived equations. H...
This paper presents a Crank–Nicolson mixed finite element method along with its reduced-order extrapolation model for a fourth-order nonlinear diffusion equation with Caputo temporal fractional derivative. By introducing the auxiliary variable...
In this study, we derive the Fokker–Planck equation for a colloidal particle subject to a harmonic trap and viscous forces under the influence of a magnetic field. We then extend the analysis to a charged colloid driven by both thermal and acti...
This paper focuses on the invariant properties of fractal operators and aims to achieve the axiomatization of the theory of fractal operators. Building upon the derivative and integral theorems of the Laplace transform, we redefine the time different...
Triaxial suction-controlled relaxation tests were performed on unsaturated reticulated red clay from a highway cut slope to quantify the coupled influence of matric suction (50–200 kPa), net confining pressure (100–300 kPa), and axial str...
Construction materials [...]
In this paper, we establish and prove two main results: (i) a Kalman-like controllability criterion, and (ii) a rank condition on the controllability matrix, defined via the discrete Mittag–Leffler function, for time-invariant linear fractional...
This paper aims to explore the numerical solution of non-linear fractional-order Burgers’-Huxley equation based on Caputo’s formulation of fractional derivatives. The equation serves as a versatile tool for analyzing a wide range of physi...
In this paper, a new class of fifth-order Chebyshev–Halley-type methods with a single parameter is proposed by using the polynomial interpolation method. The convergence order of the new method is proved. The dynamic behavior of the new method...
To reveal the deformation and failure mechanisms as well as the fracture evolution patterns of water-bearing coal–rock composites under complex stress conditions, this study established a true triaxial stress model for the key load-bearing stru...
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This paper addresses a class of multi-point initial value problems with impulses and proportional delays. The framework is based on the Atangana–Baleanu–Caputo (ABC) fractional derivative, which allows the model to incorporate hereditary...
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