Fractal and Fractional, Volume 8, Issue 11

This article mainly delves into finite-time passivity and finite-time synchronization of fractional-order spatiotemporal directed networks with multiple weights via boundary control schemes. Firstly, several concepts of finite-time passivity for frac...

In this paper, an effective numerical approach that combines the fast L1 formula and barycentric Lagrange interpolation is proposed for solving a kind of time-fractional evolution equations. This type of equation contains a nonlocal term involving th...

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called ${\mathsf{\Phi }}_s$ functions in the b-metric space...

This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this...

The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-e...

An innovative approach is utilized in this paper to solve the fractional Fokker–Planck–Levy (FFPL) equation. A hybrid technique is designed by combining the finite difference method (FDM), Adams numerical technique, and physics-informed n...

In this study, we use the integral averaging methodology, comparison with second-order differential equations, and the Riccati technique to determine the Philos-type and Hille–Nehari-type oscillation conditions of fourth-order advanced differen...

This study investigates the effect of thermal cracking on the tensile strength of granite through a combination of experimental testing and numerical simulations. The primary objective is to understand how thermal stress, induced by heat treatment at...

The impact of dynamic processes on equilibrium properties is a fundamental issue in condensed matter physics. This study investigates the intrinsic ferromagnetism generated by memory effects in the low-dimensional continuous symmetry Landau–Gin...

This paper investigates the leader-following $H_{\infty }$ consensus of fractional-order multi-agent systems (FOMASs) under input saturation via the output feedback. Based on the bounded real lemma for FOSs, the sufficient conditions of $H_{\infty }$ consensus...

Speckle noise is a granular interference that degrades image quality in coherent imaging systems, including underwater sonar, Synthetic Aperture Radar (SAR), and medical ultrasound. This study aims to enhance speckle noise reduction through advanced...

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel class of line...

Due to increasing demands on the available railway infrastructure, accurate estimates of safety-critical track condition as well as breakdowns of individual track components are crucial. This task can be supported by analyzing track measurement data....

This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the...

In this work, the practical prescribed performance tracking issue for a class of fractional-order nonlinear multiple-input multiple-output (MIMO) systems with asymmetric full-state constraints and unmeasurable system states is investigated. A neural...

Anomaly detection is crucial in large-scale industrial manufacturing as it helps to detect and localize defective parts. Pre-training feature extractors on large-scale datasets is a popular approach for this task. Stringent data security, privacy reg...

In this paper, the stability and $l_{\infty }$-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the sy...

In this paper, we present the existence of a mild solution for a class of a neutral stochastic integro-differential system over a Hilbert space. Such systems are influenced by both multiplicative and fractional noise, alongside non-instantaneous impu...

In this paper, we will introduce a compact alternating direction implicit (ADI) difference scheme for solving the two-dimensional (2D) time fractional nonlinear Schrödinger equation. The difference scheme is constructed by using the $L1-2\&m$...

By using gas physisorption and multifractal theory, this study analyzes pore structure heterogeneity and influencing factors during thermal maturation of naturally immature but artificially matured shale from the Kongdian Formation after being subjec...

This work presents an improved modelling approach for wind turbine power curves (WTPCs) using fractional differential equations (FDE). Nine novel FDE-based models are presented for mathematically modelling commercial wind turbine modules’ power...

We realize that a Sierpiński arrowhead curve (SAC) fills a Sierpiński gasket (SG) in the same manner as a Peano curve fills a square. Namely, in the limit of an infinite number of iterations, the fractal SAC remains self-avoiding, such that...

This paper proposes a fractional order integral-derivative plus second-order derivative with low-pass filters and a tilt controller called I^λDND²N²-T to improve the control performance of an automatic voltage regulator (AVR). In this study, eq...

Multifractality is a concept that helps compactly grasp the most essential features of financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded o...

Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To add...

The aim of this paper is to obtain a fractal set of ℑ-iterated function systems comprising generalized ℑ-contractions. For a variety of Hutchinson–Wardowski contractive operators, we prove that this kind of system admits a unique co...

This article examines the seasonal patterns of retail sales in the G7 nations, a key component of private consumption. Using seasonal fractional integration, we assess whether shocks present a lasting or temporary effect on retail sales trends, consi...

Realizing the integration of intelligent fruit picking and grading for apple harvesting robots is an inevitable requirement for the future development of smart agriculture and precision agriculture. Therefore, an apple maximum diameter estimation mod...

Our investigation demonstrates the necessity of mathematical modeling and design methodologies for nerve signals in the creation of artificial arms. Nerve impulses vary widely in speed; for example, unmyelinated nerves transmit impulses at around one...

The fractional differential quadrature method (FDQM) with generalized Caputo derivatives is used in this paper to show a new numerical way to solve fractional Riccati equations and fractional Lorenz systems. Unlike previous FDQM applications that hav...

With recent advancements in deep learning, spoofing techniques have developed and generative adversarial networks (GANs) have become an emerging threat to finger-vein recognition systems. Therefore, previous research has been performed to generate fi...

Fractional order filters are increasingly used due to their flexibility and continuous stepped stopband attenuation rate. The current work presents a deterministic design plan for an optimal fractional-order Legendre low-pass filter along with a stoc...

This work studies an integro-fractional differential equation (I-FrDE) with a generalized symmetric singular kernel. The scientific approach in this study was to transform the integro-differential equation (I-DE) into a mixed integral equation (MIE)...

To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis me...

This study investigates the profitability of portfolios that integrate asymmetric fractality within the Black–Litterman (BL) framework. It predicts 10-day-ahead exchange-traded fund (ETF) prices using recurrent neural networks (RNNs) based on h...

In order to quantitatively describe the influence of aggregate distribution on crack development and peak stress of recycled aggregate concrete, a multifractal spectrum theory was proposed to quantitatively characterize aggregate distribution in spec...

This paper presents a study of the application of the finite element method for solving a fractional differential filtration problem in heterogeneous fractured porous media with variable orders of fractional derivatives. A numerical method for the in...

In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This investigation may be referred to as a short memory investigation. Such concepts are useful in problems where a tra...

This article develops a simple hybrid localized mesh-free method (LMM) for the numerical modeling of new mixed subdiffusion and wave-diffusion equation with multi-term time-fractional derivatives. Unlike conventional multi-term fractional wave-diffus...

This paper investigates the exponential quasi-synchronization of fractional-order fuzzy cellular neural networks with parameters mismatch via impulsive control. Firstly, under the framework of the generalized Caputo fractional-order derivative, a new...

In this paper, we focus on the uniqueness and iterative properties of positive solution for a coupled p-Laplacian system of singular tempered fractional equations with differential order and characteristics. Firstly, the system is converted to an int...

In this work, we study the large-x asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known $H^s$-well-posedness results to the c...

The hovering flight of a quadrotor Unmanned Aerial Vehicle (UAV) refers to maintaining the aircraft in a fixed position in the air, without lateral, vertical, or rotational movements, using only the vehicle’s control systems to maintain proper...

Existing research on image-based plant classification has demonstrated high performance using artificial intelligence algorithms. However, limited camera viewing angles can cause parts of the plant to be invisible in the acquired images, leading to a...

This paper presents a quantitative study of the effects of using arbitrary-order operators in Neural Networks. It is based on a Recurrent Wavelet First-Order Neural Network (RWFONN), which can accurately identify several chaotic systems (measured by...

This paper presents a novel finite-time projective synchronization (FTPS) control strategy for fractional-order inertial memristive neural networks (FOIMNNs), exploring its application in image encryption. A sufficient condition for ensuring FTPS in...

In this paper, we propose a numerical scheme based on the shifted Legendre polynomials for solving the forced Korteweg–de Vries (fKdV) equation including a Caputo fractional operator of a distributed order. To obtain numerical solutions of thes...

Nowadays, standalone microgrids that make use of renewable energy sources have gained great interest. They provide a viable solution for rural electrification and decrease the burden on the utility grid. However, because standalone microgrids are non...

In this article, we investigate a couple of nonlinear time-fractional evolution equations, namely the cubic-quintic-septic-nonic equation and the Davey–Stewartson (DS) equation, both of which have significant applications in complex physical ph...

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristo...