Fractal and Fractional, Volume 8, Issue 6

The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models...

The present study presents a combination of two famous analytical techniques for the analytical solutions of linear and nonlinear time-fractional Emden–Fowler models. We combine the Elzaki transform (ET) and the homotopy perturbation method (HP...

To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. A...

Economic growth is resulting in serious environmental problems. Effectively establishing an economic growth model that considers environmental pollution is an important topic. To analyze the interplay between economic growth and environmental polluti...

Nano silica (NS) has been found to have a positive impact on enhancing the microporous structure of Ultra-High-Performance Concrete (UHPC). However, there is a lack of effective methods to accurately characterize the regulatory improvement mechanism...

Studying the temporal characteristics of earthquake activity contributes to enhancing earthquake prediction capabilities. The seismic b-value is a key indicator describing the relationship between seismic frequency and magnitude. This study investiga...

Space plasma turbulence is inherently characterized by anisotropic fluctuations. The generalized k-th order correlation tensor of magnetic field increments allow us to separate the mixed isotropic and anisotropic structure functions from the purely a...

The accurate recognition of a brain tumor (BT) is crucial for accurate diagnosis, intervention planning, and the evaluation of post-intervention outcomes. Conventional methods of manually identifying and delineating BTs are inefficient, prone to erro...

This article extends the celebrated Riemann–Hilbert (RH) method equipped with mixed spectrum to a new integrable system of three-component coupled time-varying coefficient complex mKdV equations (ccmKdVEs for short) generated by the mixed spect...

The pore-throat structure is a critical factor in the study of unconventional oil and gas reservoirs, drawing particular attention from petroleum geologists, and it is of paramount significance to analyze to enhance oil and gas production. In tight s...

In this paper, a fractional active disturbance rejection control (FADRC) scheme is proposed for remotely operated vehicles (ROVs) to enhance high-precision positioning and docking control in the presence of ocean current disturbances and model uncert...

We consider fractional integral operators ${(I-T)}^d,d\in (-1,1)$ acting on functions $g:{\mathbb{Z}}^{\nu }\to \mathbb{R},\nu \ge 1$, where T is the transition operator of a random walk on ${\mathbb{Z}}^{\nu }$. We obtain the sufficient and necessary conditions for the existence...

The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable...

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the...

This work presents a model for solving the Economic-Environmental Dispatch (EED) challenge, which addresses the integration of thermal, renewable energy schemes, and natural gas (NG) units, that consider both toxin emission and fuel costs as its prim...

The epidemic norovirus causes vomiting and diarrhea and is a highly contagious infection. The disease is affecting human lives in terms of deaths and medical expenses. This study examines the governing dynamics of norovirus by incorporating Lé...

The main purpose of this article is to investigate the dynamic behavior and optical soliton for the M-truncated fractional paraxial wave equation arising in a liquid crystal model, which is usually used to design camera lenses for high-quality photog...

For a class of fractional-order singular multi-agent systems (FOSMASs) with local Lipschitz nonlinearity, this paper proposes a closed-loop ${\mathcal{D}}^{\alpha }$-type iterative learning formation control law via input sharing to achieve the stable formation of FO...

In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove th...

This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrat...

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical proper...

This study addresses the issue of nonfragile state estimation for memristor-based fractional-order neural networks with hybrid randomly occurring delays. Considering the finite bandwidth of the signal transmission channel, quantitative processing is...

Under the effect of the Rosenblatt process, the well-posedness and Hyers–Ulam stability of nonlinear fractional stochastic delay systems are considered. First, depending on fixed-point theory, the existence and uniqueness of solutions are prove...

The main object of this paper is to study the traveling wave solutions of the fractional coupled Konopelchenko–Dubrovsky model by using the complete discriminant system method of polynomials. Firstly, the fractional coupled Konopelchenko–...

The foreign exchange rate market is one of the most liquid and efficient. In this study, we address the efficient analysis of this market by verifying the day-of-the-week effect with fractal analysis. The presence of fractality was evident in the ret...

In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new perf...

This study presents a comparative analysis of classical model reference adaptive control (IO-DMRAC) and its fractional-order counterpart (FO-DMRAC), which are applied to the pitch-rate control of an F-16 aircraft longitudinal model. The research demo...

In this paper, we study the existence of positive solutions for a changing-sign perturbation tempered fractional model with weak singularity which arises from the sub-diffusion study of anomalous diffusion in Brownian motion. By two-step substitution...

Distinguishing itself from marine shale formations, alkaline lake shale, as a significant hydrocarbon source rock and petroleum reservoir, exhibits distinct multifractal characteristics and evolutionary patterns. This study employs a combination of h...

The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows...

This paper addresses the enhancement of multiple Unmanned Aerial Vehicle (UAV) swarm formation control in challenging terrains through the novel fractional memetic computing approach known as fractional-order velocity-pausing particle swarm optimizat...

In this study, a class of delayed fractional-order predation models with disease and cannibalism in the prey was studied. In addition, we considered the prey stage structure and the refuge effect. A Holling type-II functional response function was us...

The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DM...

Over the last decade, dual active bridge (DAB) converters have become critical components in high-frequency power conversion systems. Recently, intensive efforts have been directed at optimizing DAB converter design and control. In particular, severa...

This paper introduces the fractional Heston-type (fHt) model as a stochastic system comprising the stock price process modeled by a geometric Brownian motion. In this model, the infinitesimal return volatility is characterized by the square of a sing...

In this paper, we prove the existence of at least two weak solutions to a class of singular two-phase problems with variable exponents involving a ψ-Hilfer fractional operator and Dirichlet-type boundary conditions when the term source is depende...

In order to achieve time–frequency superresolution in comparison to the conventional Wigner distribution (WD), this study generalizes the well-known $\tau$-Wigner distribution ($\tau$-WD) with only one parameter $\tau$ to the multiple-parameter ma...

An essential mathematical structure that demonstrates the nonlinear short-wave movement across the ferromagnetic materials having zero conductivity in an exterior region is known as the fractional stochastic Kraenkel–Manna–Merle system. I...

This work explores the existence and uniqueness criteria for the solution of hybrid Caputo–Hadamard fractional sequential differential equations (HCHFSDEs) by employing Darbo’s fixed-point theorem. Fractional differential equations play a...

In this article, we examine variational inequalities of the form $\left\{\begin{array}{c}⟨\mathcal{A}\left(u\right),v-u⟩+⟨\mathcal{F}\left(u\right),v-u⟩\ge 0,\forall v\in K\hfill \\ u\in K,\hfill \end{array}\right.$, where $\mathcal{A}$ is a generalized fractional $\mathsf{\Phi }$-Laplace operator, K is a closed co...

In this study, we investigate the application of fractional calculus to the mathematical modeling of biological systems, focusing on fractional-order-in-time partial differential equations (FTPDEs). Fractional derivatives, especially those defined in...

This study proposes an enhanced Kepler Optimization (EKO) algorithm, incorporating fractional-order components to develop a Proportional-Integral-First-Order Double Derivative (PI–(1+DD)) controller for frequency stability control in multi-area...

This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathema...

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, an...

This paper proposes a multifractal least squares support vector machine detrended fluctuation analysis (MF-LSSVM-DFA) model. The system is an extension of the traditional MF-DFA model. To address potential overfitting or underfitting caused by the fi...

The two-parameter Mittag–Leffler function $E_{\alpha ,\beta }$ is of fundamental importance in fractional calculus, and it appears frequently in the solutions of fractional differential and integral equations. However, the expense of calculating thi...

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and ($\alpha$,$\eta )$-Reich type interpolative contraction in the framework of orthogonal $\mathfrak{F}$-metric space and prove some fixed point results. Our primary result...

This paper discusses the time-fractional nonlinear Schrödinger model with optical soliton solutions. We employ the $\left(f+\left(\frac{G^{\prime }}{G}\right)\right)$-expansion method to attain the optical solution solutions. An important tool for explaining the particular explosion...

To better simulate the prices of underlying assets and improve the accuracy of pricing financial derivatives, an increasing number of new models are being proposed. Among them, the Lévy process with jumps has received increasing attention beca...

In this paper, we consider a direct problem and an inverse problem involving a nonlinear fractional diffusion equation, which can be applied to many physical situations. The equation contains a Caputo fractional derivative, a symmetric uniformly elli...