2,472 Results Found

This paper investigates the stability of continued fractions with complex partial denominators and numerators equal to one. Such fractions are an important tool for function approximation and have wide application in physics, engineering, and mathema...

The objective of this study is to reveal the intrinsic connection between fractal operators in physical fractal spaces and continued fractions. The specific contributions include: (1) reviewing fundamental concepts of continued fractions and physical...

The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy p...

The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions $H_3.$ By these relations the bran...

The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensio...

This paper considers the problem of approximating some Appell’s hypergeometric functions $F_2$ by their branched continued fraction expansions. Using the formula for the difference of two approximants of a branched continued fraction, we establish...

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of o...

In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been intr...

The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function $H_4$ ratios are cons...

In this paper, we present a systematic study of the various characteristics and properties of some continuous and discrete fractional Bessel wavelet transforms. The method is based upon the theory of the fractional Hankel transform.

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law...

In this paper, we consider continued $\beta$-fractions with golden ratio base $\beta$. We show that if the continued $\beta$-fraction expansion of a non-negative real number is eventually periodic, then it is the root of a quadratic irreducible polynomi...

In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-orde...

The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometri...

In number theory, continued fractions are essential tools because they provide distinct representations of real numbers and provide information about their characteristics. Regular continued fractions have been examined in great detail, but less rese...

We study a class of continued fraction transformations where the partial numerators are quadratic polynomials and the denominators are linear or constant. Using the Bauer–Muir transform, we establish two theorems that yield structurally distinc...

The paper presents a fractional order model of a heating process and a comparison of fractional and standard PI controllers in its closed loop system. Preliminarily, an enhanced fractional order model for the heating process on non-continuous materia...

In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the contin...

In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators. It was recently claimed that fractional-order derivatives defined...

In this work, the restricted three-body system is studied in the framework of the continuation fractional potential with its application on the Earth–Moon system. With the help of a numerical technique, we obtained thirteen equilibrium points,...

This article is a study on the $(k,s)$-Riemann–Liouville fractional integral, a generalization of the Riemann–Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furtherm...

The RSA (Rivest–Shamir–Adleman) asymmetric-key cryptosystem is widely used for encryptions and digital signatures. Let $(n,e)$ be the RSA public key and d be the corresponding private key (or private exponent). One of the attacks on RSA is...

The interpolation of Thiele-type continued fractions is thought of as the traditional rational interpolation and plays a significant role in numerical analysis and image interpolation. Different to the classical method, a novel type of bivariate Thie...

The RSA (Rivest–Shamir–Adleman) cryptosystem is an asymmetric public key cryptosystem popular for its use in encryptions and digital signatures. However, the Wiener’s attack on the RSA cryptosystem utilizes continued fractions, whic...

This study aimed to identify the effects of continuous and fractionated game formats on internal and external load in small-sided games in soccer. Twenty male professional soccer players participated in the study performing the same exercise (5 vs. 5...

This paper investigates the problem of global asymptotic stabilization of underactuated surface vessels (USVs) whose dynamics features off-diagonal inertia and damping matrices. By using input and state transformations, the dynamic model of USV is co...

Fractional calculus provides tools to model systems with memory effects; when coupled with delays, they model process histories inspired by two independent sources—the memory of the fractional derivative and the impact conditioned by the delays. This...

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT)...

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN g...

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the...

Shor’s algorithm for prime factorization is a hybrid algorithm consisting of a quantum part and a classical part. The main focus of the classical part is a continued fraction analysis. The presentation of this is often short, pointing to text b...

The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo...

Continuous-flow separation of magnetically labeled cells according to surface-marker expression levels is increasingly needed to study phenotypic heterogeneity and support downstream assays. Here, we present a microfluidic platform that uses spatiall...

This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) defini...

Leaf area index (LAI) is highly related to crop growth, and the traditional LAI measurement methods are field destructive and unable to be acquired by large-scale, continuous, and real-time means. In this study, fractional order differential and cont...

Leaf water content (LWC) is one of the important indicators of crop health. It plays an important role in the physiological process of leaves, participates in almost all physiological processes of crops, and is of great significance to the survival a...

For rapid and kinetic control-influenced resolutions, it is advisable to choose a resolving agent with the highest possible eutectic composition (ee_EuResAg). It may also be advantageous to add the crystalline resolving agent directly to the solution...

The paper deals with the problem of expansion of the ratios of the confluent hypergeometric function of N variables ${\Phi }_D^{\left(N\right)}(a,\overline{b};c;\overline{z})$ into the branched continued fractions (BCF) of the general form with N branches of branching and invest...

In this survey article, at first, the author describes how he was involved in the late 1990s on Econophysics, considered in those times an emerging science. Inside a group of colleagues the methods of the Fractional Calculus were developed to deal wi...

The increasing demand for energy-efficient hardware platforms to support artificial intelligence (AI) and machine learning (ML) algorithms in edge computing has driven the adoption of system-on-chip (SoC) architectures. Implementing neural network (N...

Background: Cardiac rehabilitation (CR) is a requisite component of care for patients with heart failure (HF). We aimed to evaluate the clinical outcomes in outpatients with HF with preserved ejection fraction (HFpEF) compared to those in patients wi...

Continuous distillation (CD) by steam is a patented emerging technology that allows us to obtain essential-oil fractions from citrus juices. It presents benefits such as reducing steam consumption by 50%, lowering environmental impact, and, by its de...

The paper discusses the prospect of using a combined model based on finite segments (polynomials) of the Volterra integral power series. We consider a case when the problem of identifying the Volterra kernels is solved. The predictive properties of t...

This is the first study to carry out a laboratory-scale assay to assess the potentiality of continuous liquid–liquid extraction with dichloromethane (CLLE_DCM) and high-power fractional distillation (HPFD) as a treatment to decontaminate the was...

In the field of Artificial Intelligence (AI) and Machine Learning (ML), a common objective is the approximation of unknown target functions $y=f\left(\mathbf{x}\right)$ using limited instances $S=({\mathbf{x}}^{\left(\mathbf{i}\right)},y^{\left(i\right)})$, where ${\mathbf{x}}^{\left(\mathbf{i}\right)}\in D$ and D represents the domain of interest. We re...

The construction of new basis functions for the Bézier or B-spline curve has been one of the most popular themes in recent studies in Computer Aided Geometric Design (CAGD). Implementing the new basis functions with shape parameters provides a differ...

The temperature regulation of nonlinear continuous stirred tank reactor (CSTR) processes remains a challenging control problem due to strong nonlinearities, time-delay effects, and sensitivity to disturbances and parameter variations. Conventional pr...

In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equatio...

The paper considers the problem of representation and extension of Appell’s hypergeometric functions by a special family of functions—branched continued fractions. Here, we establish new symmetric domains of the analytical continuation of...

In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical contin...