Fractal and Fractional, Volume 9, Issue 5

This paper introduces a highly accurate and efficient conservative scheme for solving the nonlocal damped Schrödinger system with Riesz fractional derivatives. The proposed approach combines the Fourier spectral method with the Crank–Nicol...

This study is the first to use the Bayesian Estimator of Abrupt Change, Seasonality, and Trend (BEAST) algorithm to detect trend change points in the nexuses between the green bond index (Green Bond) and WTI of crude oil, gasoline, as well as natural...

Using the multifractal detrended cross-correlation analysis (MF-DCCA) method and the Empirical Mode Decomposition (EMD)-MF-DCCA method, this study quantifies the dynamic interrelation between carbon emission allowance returns in the Chinese and EU ma...

In this paper, a new L2 (NL2) scheme is proposed to approximate the Caputo temporal fractional derivative, leading to a time-stepping scheme for the time-fractional diffusion equation (TFDE). Subsequently, the space derivative of the resulting system...

In this study, we introduce two new classes of contractions, namely enriched $(\mathfrak{I},\rho ,\chi )$-contractions and generalized enriched $(\mathfrak{I},\rho ,\chi )$-contractions, within the context of normed spaces. These classes generalize several well-known contract...

This research introduces an innovative fractal–fractional synergy framework for multiscale analysis of stress field dynamics in geo-energy systems. By integrating fractional calculus with multiscale fractal dimension analysis, we develop a coup...

In this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to...

Water pollution is a significant threat for human health, particularly in developed countries. This study advances the mathematical understanding of WP transmission dynamics by developing a fractional–fractal derivative framework with non-singu...

This work explores modern mathematical avenues as part of fractional calculus research. We apply fractional dispersion relations to the fractional wave equation to numerically examine various formulations of the generalized fractional wave equation....

Fractal dimension has proven to be a valuable tool in the analysis of geological data. For instance, it can be used for assessing the distribution and connectivity of fractures in rocks, which is important for evaluating hydrocarbon storage potential...

Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed differential equati...

The research field of clinical practice has experienced a substantial increase in the integration of information technology and control engineering, which includes the management of medication administration for general anaesthesia. The invasive natu...

This study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random...

Accurate classification of plant disease by farming robot cameras can increase crop yield and reduce unnecessary agricultural chemicals, which is a fundamental task in the field of sustainable and precision agriculture. However, until now, disease cl...

This paper investigates the strong convergence of a Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise. The existence and uniqueness of the mild solution are established via the Ba...

Eigenvalue problems play a fundamental role in many scientific and engineering disciplines, including structural mechanics, quantum physics, and control theory. In this paper, we propose a fast and stable fractional-order parallel algorithm for solvi...

Fractional differential equations (FDEs) have attracted more and more attention in the last years; among them, equations of Caputo type allow for “more natural” initial conditions when the order is greater than one. As a result, many nume...

The experimental study of shale fracture development is very important. As a channel of permeability, a fracture has a great influence on the development of shale gas. This study presents the results of a fracture evaluation in the Silurian Longmaxi...

This study proposes a novel image segmentation method, MF-DFA combined with the Allen–Cahn equation (MF-AC-DFA). By utilizing the Allen–Cahn equation instead of the least squares method employed in traditional MF-DFA for fitting, the accu...

Magneto-electro-elastic materials, a novel class of smart materials, exhibit remarkable energy conversion properties, making them highly suitable for applications in nanotechnology. This study focuses on various aspects of the fractional nonlinear lo...

In this paper, we study the existence of extremal solutions for a Caputo-type fractional-order initial value problem. By using the monotone iteration technique and the upper–lower solution method, we obtain our existence theorem when the nonlin...

For a self-affine iterated function system (IFS) ${\left\{f_j\right\}}_{j=1}^N$ on ${\mathbb{R}}^d$ defined by $f_j\left(x\right)=A^{-1}(x+d_j)$, where A is an expansive matrix and $d_j\in {\mathbb{R}}^d$, we reveal a novel characterization of the open set and weak separation conditions through the bounded deg...

The coronavirus (COVID-19) expanded rapidly and affected almost the whole world since December 2019. COVID-19 has an unusual ability to spread quickly through airborne viruses and substances. Taking into account the disease’s natural progressio...

Gravity water waves in the shallow-ocean scenario described by generalized Boussinesq–Broer–Kaup–Whitham (gBBKW) equations are discussed. The residual symmetry and Bäcklund transformation associated with the gBBKW equations are...

The authors consider a nonlinear $\psi$-Hilfer fractional-order Volterra integro-differential equation ($\psi$-Hilfer FrOVIDE) that incorporates N-multiple variable time delays into the equation. By utilizing the $\psi$-Hilfer fractional derivative, the...

This paper conducts an in-depth investigation into the fundamental relationship between the fractal dimensions and convergence properties of mathematical sequences. By concentrating on three representative classes of sequences, namely, the factorial-...

This manuscript tries to show that there is only one solution to the problem of the q-Hilfer fractional generalized pantograph differential equations with a nonlocal condition, and it does so by employing a particular technique known as Schaefer&rsqu...

In this work, we first develop the modified time Caputo fractional Kawahara Equations (MTCFKEs) in the usual Hilbert spaces and extend them to analogous structures within the theory of Hilbert algebras. Next, we employ the residual power series metho...

China currently faces critical climatic conditions, with persistent global warming trends and extreme heat waves across the northern hemisphere. To explore the predictive trajectory of regional extreme high temperature influenced by groundwater over-...

The main purpose of this article is to study the optical solutions of the nonlinear Kodama equation with the M-truncated derivative by using the extended $(G^{\prime }/G)$-expansion method. Firstly, the nonlinear Kodama equation with the M-truncated deriv...

This study aims to explore the effect of spatial-fractional derivatives and the multiplicative standard Wiener process on the solutions of the stochastic fractional regularized long-wave equation (SFRLWE) and contribute to its analysis. We introduce...

This article considers a class of Caputo fractional-order fuzzy cellular neural networks (CFOFCNNs) with transmission delays and uncertain perturbations. In particular, nonlinear activations and fuzzy operators AND and OR are investigated in the driv...

This paper presents a modified Euler—Maruyama (EM) method for mixed stochastic fractional integro—differential equations (mSFIEs) with Caputo—type fractional derivatives whose coefficients satisfy local Lipschitz and linear growth c...

The main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the pre...

Base excitation sources significantly impact vehicle-body vibrations in maglev systems, with the dynamic performance of the suspension system playing a crucial role in mitigating these effects. The second-series suspension system of a maglev vehicle...

This study investigates the multifractal behavior of four leading semiconductor stocks—Intel (INTC), Advanced Micro Devices (AMD), Nvidia (NVDA), and Broadcom (AVGO)—in relation to key financial assets, including the Dow Jones Industrial...

To investigate the pore structure evolution characteristics and damage mechanism of sandstone subjected to treatment with freeze–thaw cycles, quantitative analyses were conducted on the longitudinal wave velocity (LWV) and T₂ spectrum of sandst...

This paper is dedicated to elucidating the abstract algebraic structure of operational calculus theory. Based on abstract algebra and operational calculus, the operator algebra theory of Mikusiński has been revised. We restate the concept of Mik...

Comprehensive assessment of pore structure and multiphase water distribution is critical to the flow and transport process in coalbed methane (CBM) reservoirs. In this study, nuclear magnetic resonance (NMR) and multifractal analysis were integrated...

In this work, we investigate the extended numerical discretization technique for the solution of fractional Bernoulli equations and SIRD epidemic models under the Caputo fractional, which is accurate and versatile. We have demonstrated the method&rsq...

Fractional multi-delay differential systems, as an important mathematical model, can effectively describe viscoelastic materials and non-local delay responses in ecosystem population dynamics. It has a wide and profound application background in inte...

This study uses a conformable derivative of order $\beta$ to investigate a fractional Whitham–Broer–Kaup ($\mathcal{FWBK}$) model. This model has significant uses in several scientific domains, such as plasma physics and nonlinear optics. The enhanced...

The $L1$ scheme on a modified graded mesh is proposed to solve a Caputo–Hadamard fractional diffusion equation with order $\alpha \in (0,1)$. Firstly, an improved graded mesh frame is innovatively constructed, and its mathematical properties are...

This article investigates the qualitative analysis and traveling wave solutions of a (3 + 1)-dimensional generalized nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt system. This equation is commonly used to simulate nonlinear wave problems in the...

The Cauchy problem for the Laplace equation in an annular bounded region consists of finding a harmonic function from the Dirichlet and Neumann data known on the exterior boundary. This work considers a fractional boundary condition instead of the Di...

The acidification modification of coal seams is a significant technical measure for transforming coalbed methane reservoirs and enhancing the permeability of coal seams, thereby improving the extractability of coalbed methane. However, the acids curr...

In this paper, we investigate the dynamics of the generalized Chen–Lee–Liu (gCLL) equation utilizing the Riemann–Hilbert method to derive its $\mathit{N}$-soliton solution. We incorporate a self-steepening term and a Kerr nonlinear term to cha...

This study introduces a novel generalized class of special polynomials using a fractional operator approach. These polynomials are referred to as the generalized Gould–Hopper–Bell-based Appell polynomials. In view of the operational metho...

In this paper, our primary objective is to develop a robust and efficient higher-order structure-preserving algorithm for the numerical solution of the two-dimensional nonlinear spatial fractional Schrödinger equation. This equation, which incor...

In this paper, we propose an approach for constructing quasiparticle-like asymptotic solutions within the weak diffusion approximation for the generalized population Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation,...