Fractal and Fractional, Volume 10, Issue 3

In this work, we provide a convolution type operator ${\mathsf{\Lambda }}_{\nu ,b}$ that is produced by the generalized Marcum Q-function and examine how it maps to various Janowski-type subclasses of harmonic univalent functions. Since the Marcum Q-function has an...

Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly d...

This paper investigates the fractal dynamical behavior of a discrete Caputo fractional-order hepatitis C virus model. First, we analyze the stability of the system by using spectral radius and design the fractional-order controller based on coordinat...

This paper addresses the stabilization problem for a class of fractional-order memristive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays under an intermittent boundary control framework. Two scenarios are cons...

Econophysics is an interdisciplinary field that applies physics concepts to economic and financial systems. By utilizing tools such as statistical physics, including fractal analysis and entropy measures, econophysics helps model the complex and non-...

Prolonged water injection in unconsolidated sandstone reservoirs can induce pore rearrangement and modify flow pathways, thereby affecting reservoir performance. However, quantitative characterization of pore evolution in both temporal and spatial di...

In this article, we investigate the existence and approximate controllability of a class of Sobolev-type fractional stochastic differential equations of order $1<\delta <2$ with infinite delay. The analysis is carried out in an abstract Hilbert s...

The fractional Fourier transform (FRFT) serves as an effective tool for linear frequency modulated (LFM) signal parameter estimation, whose performance depends on the search efficiency for the optimal transform order. To address the issues of fixed i...

This paper investigates a class of coupled $\psi$-Hilfer fractional pantograph–Langevin equations with nonlocal integral boundary conditions. By reformulating the problem as an equivalent fixed point equation and employing Mönch’s fix...

Unmanned Aerial Vehicles (UAVs) are widely used in fields such as autonomous missions, reconnaissance, surveillance, and various industrial applications. These vehicles can perform desired tasks without human intervention in challenging environmental...

Sleep disorders are prevalent in the world, and they lead to severe health issues such as cardiovascular disease and cognitive disabilities. Conventional polysomnography-based diagnosis is based on manual EEG analysis under the supervision of trained...

Fractional calculus, with conceptual origins tracing back to the foundational dialogues between L’Hôpital and Leibniz in 1695, has undergone a remarkable transformation from abstract mathematical inquiry into a key framework for studying...

This paper mainly considers the fractional parameter identification algorithms of the bilinear-in-parameter autoregressive (AR-BIP) system. The data filtering technique is introduced to improve the parameter estimation accuracy of the AR-BIP system,...

The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contrib...

Rolling bearing faults are the primary cause of rotating machinery failure. Under complex operating conditions, the weak fault impact signals are easily overwhelmed by strong noise and exhibit significant non-stationary characteristics, posing severe...

The full-bridge LLC resonant converter is one of the most suitable converters for high-power, high-efficiency applications. Although the design methodologies for full-bridge LLC resonant converters are already well-established, the development of the...

This paper studies an inverse problem associated with the time-fractional Schrödinger equation in a field-free potential. To address the severe ill-posedness of the problem, a mollification regularization method with truncated kernels is employe...

Precise and smooth actuation is a central requirement in surgical robotics, where small tracking errors or oscillations can directly affect task quality and safety. This paper studies the control of an induction-motor-driven surgical joint using a sl...

This study presents a comprehensive investigation of exact fractional wave solutions and bifurcation analysis for the (3 + 1)-dimensional extended shallow water wave (3D-eSWW) equation with $\beta$-derivative, which models nonlinear wave phenomena in...

This study examines a comprehensive class of coupled nonlinear $\varrho$-Hilfer fractional neutral impulsive integro-differential systems with mixed delays and non-local initial conditions. The primary contribution of this study is the creation of a unified...

This article deals with the global existence and uniqueness of solutions to a fractional-order SIQR epidemic model, alongside its intricate chaotic and complex dynamics as functions of the fractional order. The well-posedness of the model solutions,...

Tight sandstone reservoirs are characterized by highly heterogeneous pore structures, in which multiscale pore–throat systems jointly control the shapes of capillary pressure curves and relative permeability, thereby exerting a fundamental infl...

Robust controller tuning is essential for the accurate regulation of nonlinear dynamic plants operating under variable conditions. This study proposes an enhanced gradient-based optimizer, termed the quadratic wavelet–enhanced gradient-based op...

When bridge towers are subjected to strong winds, they exhibit significant displacements. This displacement change can serve as an important indicator for structural performance warning. The displacement and acceleration collected in real time by the...

This work constructs an orthogonal function system on bounded intervals $[0,R]$ associated with the Atangana–Baleanu–Caputo (ABC) fractional derivative for $\alpha \in (1/2,1)$. Starting from a fractional Laguerre-type equation involving th...

This study explores the interconnection between the variables of ChatGPT usage, energy consumption, water consumption, and carbon dioxide CO₂ emissions. A new integer and fractional order model using the Caputo derivative is proposed to comprehend th...

The large-scale rapid deployment of renewable generation and energy storage is transforming traditional power system dynamics through intermittency, reduced inertia, and pronounced long-range temporal dependence. Existing power system modeling framew...

As a core non-mechanical beam-steering device, cascaded liquid crystal polarization gratings (CLCPGs) suffer from insufficient pointing accuracy due to inherent fabrication and assembly errors, which must be compensated by liquid crystal optical phas...

This comprehensive review examines the application of fractal theory and technology in the study of cementitious materials, with a focus on cement and concrete. We begin by introducing the fundamental concepts of fractal geometry and the various frac...

This paper develops a functional operator-theoretic framework for nonlinear Erdelyi–Kober (EK) fractional dynamical systems formulated in Banach spaces endowed with the compact-open topology. Within this setting, sufficient conditions for exist...

Lacustrine shales are key targets for shale oil exploration, yet the quantitative characterization of their complex and heterogeneous pore systems remains a significant challenge, constraining effective reservoir evaluation and development. This stud...

The development of fractal set theory has been strongly driven by the introduction of new classes of fractal sets, among which the attractors of iterated function systems (IFSs) play a central role. In this work, we study a generalization of the clas...

In this paper, we developed and constructed the Haar wavelet (HW) for the two-dimensional (2D) time-fractional neuronal dynamics model (TFNDM) with the dynamical electro-diffusion behaviour of ions in nerve cells. The Haar wavelet method is considere...

This study investigates the dynamics of a delayed fractional-order competition-competition-cooperative system with Beddington–DeAngelis functional responses. First, we prove the boundedness and uniqueness of the solutions. We analyze the existe...

This paper presents a novel mathematical framework for anthrax transmission by integrating Caputo fractional derivatives, distributed delays, and a Beddington–DeAngelis incidence function. The proposed model captures memory effects in disease p...

Fractal dimension is widely used as a quantitative descriptor of structural complexity in digital images. However, its practical implementation often involves methodological and computational trade-offs. The compression-based estimator provides an in...

Accurate characterization of water saturation in tight sandstone gas reservoirs is the key to reservoir evaluation and productivity prediction. In view of the limitations of the traditional Archie formula in describing the strongly heterogeneous pore...

The Internet of Things (IoT) faces critical security challenges stemming from resource-constrained devices and inadequate intrusion detection capabilities. Traditional machine learning approaches struggle with high-dimensional network traffic data du...

In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented...

The concept of fuzzy differential subordination was introduced in 2011 as a natural generalization of classical differential subordination, reflecting the contemporary trend of incorporating fuzzy set theory into well-established mathematical framewo...

Human physiology is among the most complex systems in nature, characterized by intricate structural and functional networks and rich temporal dynamics. Electrophysiological signals produced by different tissues/organs reflect physiological activity,...

In this work, we derive necessary optimality conditions for a class of fractional variational problems involving Caputo-type derivatives. We consider functionals defined on appropriate spaces of absolutely continuous functions and study both periodic...

This paper investigates the effectiveness of integrating a matrix converter (MC) into a wind turbine system based on a Doubly Fed Induction Generator (DFIG), focusing on the indirect control of active and reactive power using fractional regulators. T...

This study addresses high water cut and low recovery in bottom-water sandstone reservoirs by optimizing CO₂ and N₂ foam flooding parameters. The key innovation is the pioneering application of fractal dimension to quantitatively characterize water co...

In this paper, we study a nonlinear system of sequential Caputo fractional differential equations equipped with coupled mixed multi-point boundary conditions. In particular, the boundary conditions involve the values of the unknown functions at the e...

In the present work we introduce an appropriate definition of the notion of a Lagrange (formal) adjoint system for homogeneous systems with incommensurate-order derivatives in Caputo’s sense and distributed delays. Under natural conditions, the...

Multi-criteria decision-making (MCDM) involves evaluating alternatives under uncertain, vague, and conflicting criteria. While fuzzy set theories, such as intuitionistic, pythagorean, fermatean, and q-rung orthopair fuzzy sets have advanced uncertain...

This paper investigates the fully distributed observer-based dynamic double-event-triggered bipartite consensus tracking problem of fractional-order multi-agent systems (FOMASs) with input saturation under a directed graph. First, to address this com...

Marine concrete is often exposed to multiple aggressive ions, so mechanical deterioration cannot be reliably interpreted using single-ion durability concepts. This study investigates ocean-oriented concretes incorporating high contents of mineral adm...

Granular materials subjected to complex stress histories exhibit pronounced path dependence, multi-scale heterogeneity and scale-invariant characteristics, especially when particle breakage leads to gradation evolution with fractal features. Discrete...