This paper explores the extension of classical transforms to fractal spaces, focusing on the development and application of the Fractal Hankel Transform. We begin with a concise review of fractal calculus to set the theoretical groundwork. The Fracta...
This paper focuses on the invariant properties of fractal operators and aims to achieve the axiomatization of the theory of fractal operators. Building upon the derivative and integral theorems of the Laplace transform, we redefine the time different...
This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing
By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral ope...
This study introduces a novel analytical technique known as the double local fractional Yang–Laplace transform method (
This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effe...
In this paper, a new method for analysing gastroesophageal reflux disease (GERD) is shown. This novel method uses wavelet transform (WT) and wavelet-based fractal analysis (WBFA) on esophageal pH-metry measurements. The esophageal pH-metry is an impo...
This paper addresses the extension of Martinez–Kaabar (MK) fractal–fractional calculus (for simplicity, in this research work, it is referred to as MK calculus) to the field of integral transformations, with applications to some solutions...
Vision Transformers achieve strong performance across computer vision tasks but suffer from quadratic computational complexity with respect to token count, limiting deployment in resource-constrained environments. Existing token pruning methods rely...
This paper presents a mathematical analysis of semantic convergence in transformer-based language models, drawing inspiration from the concept of fractal self-similarity. We introduce and prove a novel theorem characterizing the gradient of embedding...
The growing reliance on digital banking and financial transactions has brought significant security challenges, including data breaches and unauthorized access. This paper proposes a robust method for enhancing the security of banking and financial t...
A fractional-order image enhancement and fractal complexity-guided fusion method was developed to improve weak fault representation and introduce complexity-aware priors into dissolved gas analysis (DGA)-based diagnosis of oil-immersed power transfor...
In this manuscript, the nonlinear Burgers equations are studied via a fractal fractional (FF) Caputo operator. The results of coupled fixed point theorems in cone metric space are used to discuss the uniqueness of solution to the proposed coupled equ...
In this work, the Renormalization Method (RM) is used to analyze the dynamics of a nonlinear two-degree-of-freedom (2DOF) system under parametric excitation, with a focus on fractal vibration behavior. This procedure comprises transforming the system...
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the lo...
We extend the classical fractal uncertainty principle (FUP) framework in time-frequency analysis by exploring several novel directions. First, we generalize the FUP beyond the classical Gaussian window by investigating non-Gaussian windows and the co...
The core challenge of high-precision medical image segmentation lies in modeling the multi-scale fractal self-similarity of human abdominal organs and cardiac structures, especially the blurred boundaries and weak features of low-contrast tissues. Ex...
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace trans...
The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving comp...
In order to further research the relationship between fractals and complicated networks in terms of self-similarity, the uniform convergence property of the sequence of fractal interpolation functions which can generate self-similar graphics through...
The skid resistance of asphalt pavement is vital for traffic safety and reducing accidents. Existing research using only wavelet transforms or fractal theory to study the pavement surface texture-skid resistance relationship has limitations. This pap...
In coal dry screening, online detection for screening efficiency is a significant challenge. Notwithstanding, the method of image processing is strenuous to implement in this field due to the complex surface texture of shattered coal. This method ide...
Multi-focus image fusion is an important method for obtaining fully focused information. In this paper, a novel multi-focus image fusion method based on fractal dimension (FD) and parameter adaptive unit-linking dual-channel pulse-coupled neural netw...
Plant diseases, being a subject of interdisciplinary research, significantly reduce crop yield, quality, and economic returns, while the misidentification of pathogens often leads to ineffective treatments and may harm beneficial organisms and ecosys...
A number of mathematical methods have been developed to make temporal signal analyses based on time series. However, no effective method for spatial signal analysis, which are as important as temporal signal analyses for geographical systems, has bee...
Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal al...
In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation...
This study investigates the impact response of polymer foams commonly used in protective packaging, considering the fractal nature of their material microstructure. The research begins with static material characterization and impact tests on two low...
Accurate carbon market price prediction is crucial for promoting a low-carbon economy and sustainable engineering. Traditional models often face challenges in effectively capturing the multifractality inherent in carbon market prices. Inspired by the...
In this manuscript, we investigate the nonlinear Boussinesq equation (BEQ) under fractal-fractional derivatives in the sense of the Caputo–Fabrizio and Atangana–Baleanu operators. We use the double modified Laplace transform (LT) method t...
The pivotal proposal of this work is to present a reliable algorithm based on the local fractional homotopy perturbation Sumudu transform technique for solving a local fractional Tricomi equation occurring in fractal transonic flow. The proposed tech...
This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function
This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system...
As a key concern in a power system, a deteriorated insulation is likely to bring about a partial discharge phenomenon and hence degrades the power supply quality. Thus, a partial discharge test has been turned into an approach of significance to prot...
To address the limitations of traditional tumor diagnostic methods in image feature extraction and model generalization, this study innovatively proposes a synergistic diagnostic model that integrates fractional Fourier transform (FrFT) and error bac...
In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whith...
Multi-focus image fusion is a popular technique for generating a full-focus image, where all objects in the scene are clear. In order to achieve a clearer and fully focused fusion effect, in this paper, the multi-focus image fusion method based on th...
The properties of pulsed laser deposited of Ni60Ti40 shape memory thin films generated in various deposition conditions were investigated. In-situ plasma monitoring was implemented by means of space- and time-resolved optical emission spectroscopy, a...
In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model. First, a fractional transformation i...
Passive acoustic monitoring (PAM) is a valuable tool for ecological research, but many eco-acoustic indices show inconsistent correlations with biodiversity due to methodological variability and environmental noise. We propose a complementary, physic...
In this work, two novel methodologies for the multiband spectrum sensing in cognitive radios are implemented. Methods are based on the continuous wavelet transform (CWT) and the multiresolution analysis (MRA) to detect the edges of available holes in...
The development and deployment of sensors for undersea cabled observatories is presently biased toward the measurement of habitat variables, while sensor technologies for biological community characterization through species identification and indivi...
Specifying the role of genetic mutations in cancer development is crucial for effective screening or targeted treatments for people with hereditary cancer predispositions. Our goal here is to find the relationship between a number of cancerogenic mut...
The ATLAZUL project is an Interreg effort among 18 partners from Spain and Portugal along the Atlantic Iberian coasts. One of its objectives is the development of new methods and data processing for oceanic information to produce useful products for...
This paper addresses the extension of the Martinez–Kaabar fractal–fractional calculus (simply expressed as MK calculus) to the context of reduced differential transformation, with applications to the solution of some partial differential...
The Heilongjiang Duobaoshan area is located at the confluence of the Great Xing’an Range and the Lesser Xing’an Range, and the area has undergone a complex magmatic and tectonic evolutionary history resulting in a complex and diverse geol...
26 April 2021
Rapid urbanization in China has transformed many rural areas from agriculture-dominated to diverse systems, but studies of rural morphology are limited compared to studies of urban settlement. This paper uses a fractal dimension (FD) value to analyze...
Centered polygonal lacunary functions are a type of lacunary function that exhibit behaviors that set them apart from other lacunary functions, this includes rotational symmetry. This work will build off of earlier studies to incorporate the automorp...
In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function
The prevention of excessive pressure build-up in pipelines requires a thorough understanding of water hammer phenomena. Using theoretical techniques, researchers have investigated this phenomenon and proposed productive solutions. In this article, we...
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