In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational cont...
In this study, we introduce an innovative proximity-based approach to fractals using a proximal iterated function system generated by a finite set of generalized proximal contractions (Prox-GC-IFS). Thus, as a novel method to create fractals, we pres...
In this paper, we obtain multifractals (attractors) in the framework of Hausdorff b-metric spaces. Fractals and multifractals are defined to be the fixed points of associated fractal operators, which are known as attractors in the literature of fract...
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 paper investigates the existence of common attractors for generalized
In order to obtain the automatic simulation generation of traditional handmade batik patterns in a computer, this paper proposes the automatic generation method of batik flower patterns based on fractal geometry. Firstly, we analyze the fractal chara...
This paper investigates a class of nonlinear rational difference equations with delayed terms, which often arise in various mathematical models. We analyze the iterative behavior of these rational functions and show how their iterations can be repres...
This paper develops an extension of the research work by Proinov to the product spaces
An iterated function system consists of a complete metric space
This study develops a hybrid fractal–parametric modeling (HFPM) workflow integrating recursive affine iterated-function systems, finite-scale box-counting, fixed-thickness prism extrusion, and NSGA-II to explore trade-offs between geometric mat...
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...
The theory of iterated function systems (IFSs) has been an active area of research on fractals and various types of self-similarity in nature. The basic theoretical work on IFSs has been proposed by Hutchinson. In this paper, we introduce a new gener...
This paper introduces a complete
The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal antennas, is studied. In particular, their entropy is...
The Koch curve was first described by the Swedish mathematician Helge von Koch in 1904 as an example of a continuous but nowhere differentiable curve. Such functions are now characterised as fractal since their graphs are in general fractal sets. Fur...
For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as these fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we introduce...
Self-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary sc...
Julia and Mandelbrot sets are fundamental objects in fractal geometry and complex dynamical systems. Their generation commonly relies on escape-time algorithms combined with iterative schemes. While previous studies have mainly considered generalized...
We propose a novel approach to fractals by leveraging the approximation of fixed points, emphasizing the deep connections between fractal theory and fixed-point theory. We include a condition of isomorphism, which not only generates traditional fract...
A nonlinear equation
In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filte...
In this paper, we introduce the concept of a
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...
Fractional-order differential equations are powerful tools for the representation of dynamic systems that exhibit long-term memory effects. The verified simulation of such system models with the help of interval tools allows for the computation of gu...
This paper explores the generalization of the fixed-point theorem for Fisher contraction on controlled metric space. The controlled metric space and Fisher contractions are playing a very crucial role in this research. The Fisher contraction on the c...
To describe stationary physical systems, well-known boundary problems for shielded Poisson and Sophie Germain equations are used. The obtained shielded harmonic and biharmonic systems are approximated using the finite element method and fictitiously...
A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to nonlinear systems of equations hold...
Newton’s iteration is a fundamental tool for root-finding and numerical solutions of systems of equations. The iteration rapidly refines the initial approximation to the exact root, and in general, the convergence is quadratic. Since the method...
In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Boh...
We are interested in modelling smaller datasets to generate more accurate, sub-regional or regional climate forecasts. The focus of this paper is to present the findings of a study investigating the application of empirical mode decomposition (EMD) t...
This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first gene...
In this paper, an efficient iterative method based on the generalized multiscale finite element (Iter-GMs) method is applied to solve the distributed optimal control problems governed by stochastic parabolic equations. Within this framework, we first...
In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet...
In the traditional iterative learning control (ILC) method, the operational time interval is conventionally fixed to facilitate a seamless learning process along the iteration axis. However, this condition may frequently be contravened in real-time a...
In this article, firstly, an overview of affine fractal interpolation functions using a suitable iterated function system is presented and, secondly, the construction of Bernstein affine fractal interpolation functions in two and three dimensions is...
We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspa...
A new family of iterative methods for solving systems of nonlinear equations is introduced, extending and unifying several existing approaches within a general framework. In the single-variable case, Newton’s method was accelerated using Pad&ea...
Centralized and distributed optimization methods used by traditional virtual power plants (VPPs) in power system dispatching face issues such as high computational complexity, difficulties in privacy protection, and slow iterative convergence. There...
This paper presents a meshless collocation technique for the fourth-order transient stream function formulation of the Navier–Stokes equations. The technique employs a hybrid kernel function and is augmented by the ghost point method and Picard...
Aiming to address the defects of the arithmetic optimization algorithm (AOA), such as easy fall into local optimums and slow convergence speed during the search process, an improved arithmetic optimization algorithm (IAOA) is proposed and applied to...
A prerequisite for establishing fusion power as one of the sources for low-carbon electricity generation is the demonstration of the capability of future fusion power plants in achieving tritium self-sufficiency and its capability of efficiently prod...
We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of d...
We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson oper...
Formal methods are crucial in program specification and verification. Instead of building cases to test functionalities, formal methods specify functionalities as properties and mathematically prove them. Nevertheless, the applicability of formal met...
The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit...
In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight...
In this manuscript, we explore stunning fractals as Julia and Mandelbrot sets of complexvalued cosine functions by establishing the escape radii via a four-step iteration scheme extended with s-convexity. We furnish some illustrations to determine th...
Asynchronous iterations have long been used in distributed computing algorithms to produce calculation methods that are potentially faster than a serial or parallel approach, but whose convergence is more difficult to demonstrate. Conversely, over th...
Product design constitutes an iterative process centered on user requirements. In this process, user requirements are collected, interpreted by designers and transformed into design objectives, which are then refined through solution generation and e...
The geomagnetic matching aided positioning system based on Iterative Closest Contour Point (ICCP) algorithm can suppress the accumulation error of the inertial navigation system and achieve the accurate positioning of the vehicle. Aiming at the probl...
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