Fractal and Fractional, Volume 8, Issue 10

This paper focuses on the fuzzy adaptive predefined-time control for fractional-order nonlinear systems with time-varying deferred constraints. First, a modified dynamic surface control technique is introduced to address the problem of computational...

Industrial mobile robots easily experience actuator loss of some effectiveness and additive bias faults due to the working scenarios, resulting in unexpected performance degradation. This article proposes a novel adaptive fault-tolerant control (FTC)...

Contact interface is essential for the dynamic response of the bolted structures. To accurately predict the dynamic characteristics of bolted joint structures, a fractal extension of the segmented scale model, i.e., the JK model, is proposed in this...

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T&...

We introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering...

In this paper, we consider constructions of first derivative approximations using the generating function. The weights of the approximations contain the powers of a parameter whose modulus is less than one. The values of the initial weights are deter...

This research introduces a fractional high-order sliding mode control (FHOSMC) method that utilises an inverse integral fractional order, $0<\beta <1$, as the high order on the FHOSMC reaching law, exhibiting a novel contribution in the related f...

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional...

This paper addresses critical gaps in the digital implementations of fractional-order memelement emulators, particularly given the challenges associated with the development of solid-state devices using nanomaterials. Despite the potentials of these...

This study examines the effectiveness of Convolutional Autoencoder (CAE) and Variational Autoencoder (VAE) models in detecting anomalies within occupational accident data from the Mining of Coal and Lignite (NACE05), Manufacture of Other Transport Eq...

This paper explores the fractal properties of token embedding spaces in GPT-2 language models by analyzing the stability of the correlation dimension, a measure of geometric complexity. Token embeddings represent words or subwords as vectors in a hig...

This paper establishes a unique approach known as the multi-generalized Laplace transform decomposition method (MGLTDM) to solve linear and nonlinear dispersive KdV-type equations. This method combines the multi-generalized Laplace transform (MGLT) w...

The aim of this paper is to identify a time-independent source term in the Rayleigh–Stokes equation with a fractional derivative where additional data are considered at a fixed time point. This inverse problem is proved to be ill-posed in the s...

The global incidence of cutaneous squamous cell carcinoma (cSCC), a prevalent and aggressive skin cancer, has risen significantly, posing a substantial public health challenge. This study investigates the tumor microenvironment (TME) of cSCC by focus...

In this work, a fractional consistent Riccati expansion (FCRE) method is proposed to seek soliton and soliton-cnoidal solutions for fractional nonlinear evolutional equations. The method is illustrated by the time-fractional extended shallow water wa...

In the present work, we study some existing results related to a new class of Steklov $p\left(x\right)$-Kirchhoff problems with critical exponents. More precisely, we propose and prove some properties of the associated energy functional. In the first existence re...

The emission of carbon dioxide is the main reason for many global warming problems. Although China has made tremendous efforts to reduce carbon emission, the space–time dynamics of the carbon emission trend is still imbalanced. To forecast CDED...

Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with...

In this paper, the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise is investigated with consideration of a new method for dealing with singular integrals. Firstly, the estimate on higher moments...

In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CN...

In this article, exact solutions of the Biswas–Arshed equation are obtained using the extended Weierstrass transformation method (EWTM). This method is widely used in solid-state physics, electrodynamics, and mathematical physics, and it yields...

This paper investigates the explicit, accurate soliton and dynamic strategies in the resolution of the Wazwaz–Benjamin–Bona–Mahony (WBBM) equations. By exploiting the ensuing wave events, these equations find applications in fluid d...

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some...

In this paper, using the properties of the conformable fractional difference and fractional sum, we initially establish some oscillatory and asymptotic criteria for a fifth-order fractional difference equation. Several critical inequalities, the Ricc...

At present, the integration of microgrids into power systems presents significant power quality challenges in terms of the rising adoption of nonlinear loads and electric vehicles. Ensuring the stability and efficiency of the electrical network in th...

The pore structure and mineral characteristics affect the accumulation and migration of hydrocarbons in shale, which determines the production capacity of shale oil. In this study, shale samples from the Chang 7 member of the Ordos Basin in China wer...

The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequal...

Norovirus is a leading global cause of viral gastroenteritis, significantly affecting mortality, morbidity, and healthcare costs. This paper develops and analyzes a stochastic $\mathsf{S}\mathsf{E}\mathsf{I}\mathsf{Q}\mathsf{R}$ epidemic model for norovirus dynamics, incorporating temporal immuni...

This paper explores the exact solutions of the fractional Hirota–Satsuma coupled KdV (fHScKdV) equation in the Beta fractional derivative. The logistic method is first proposed to construct analytical solutions for the fHScKdV equation. In orde...

A fractal–fractional calculus is presented in term of a generalized gamma function (ℓ−gamma function: ${\Gamma }_{\mathit{\ell }}(.)$). The suggested operators are given in the symmetric complex domain (the open unit disk). A novel arrangement of...

Using fractal analysis and computing fractal dimension to understand materials chemistry and solve problems such as catalysis, chemical reactions, fuel storage, and material design is an important scientific research domain [...]

Developing two-step fractional numerical methods for finding the solution of nonlinear equations is the main objective of this research article. In addition, we present a detailed study of convergence analysis for the methods that have been proposed....

In this paper, we consider a class of fractional Schrödinger–Poisson systems ${(-\mathsf{\Delta })}^{s}u+\lambda V(x)u+\varphi u=f(u)+{|u|}^{2_s^{*}-2}u$ and ${(-\mathsf{\Delta })}^t\varphi =u^2$ in ${\mathbb{R}}^3$, where $s,t\in (0,1)$ with $2s+2t>3$, $\lambda >0$ denotes a...

The application of high-pressure fluid induces the closure of isolated pores inside the matrix and promotes the generation of new fractures, resulting in a compressive effect on the matrix. To examine the compressibility of coal-measure shale samples...

The article presents a novel control strategy for cable-driven aerial manipulators (UAMs) aimed at enhancing impedance control during contact operations in complex environments. A fractional-order nonsingular terminal sliding mode control (FONTSMC) i...

Spherical glass beads weaken the influences of particle morphology, surface properties, and microscopic fabric on shear strength, which is significant for revealing the relationship between macroscopic particle friction mechanisms and the particle si...

The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted...

Inherent constant Q attenuation can be described using fractional Laplacian operators. Typically, the fractional Laplacian viscoacoustic or viscoelastic wave equations are addressed utilizing the staggered-grid pseudo-spectral (SGPS) method. However,...

This paper is devoted to building a general framework for constructing a solution to fractional Phi-4 differential equations using a Caputo definition with two parameters. We briefly introduce some definitions and properties of fractional calculus in...

This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linea...

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates di...

Faults, as a kind of fracture tectonics, play a role in reservoir closure or provide oil and gas transportation channels. The accurate understanding of the distribution characteristics of faults is significant for oil and gas exploration. The traditi...

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do...

The accurate characterization of soil structure is fundamental to groundwater science, environmental ecology, and Earth systems science. To address the challenge of quantifying the high spatial variability of large-scale soil structures, this study u...

This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innov...

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the sy...

In this paper, we propose a non-convex model with fractional-order applied to image deblurring problems. In the new model, fractional-order gradients have been introduced to preserve detailed features, and a source term with a blurry kernel is used f...

This paper introduces a new mathematical modelling method of a thermoelastic and electromagnetic half-space in the context of four different thermoelastic theorems: Green–Naghdi type-I, and type-III; Lord–Shulman; and Moore–Gibson&n...

In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In...

To construct Caputo fractional-order time-delayed cellar neural networks (FOTDCNNs) that characterize real environments, this article introduces partial uncertainties, fuzzy operators, and nonlinear activation functions into the network models. Speci...