1,519 Results Found

In this paper, we study the approximation properties of some exponential and semi-exponential operators. We focus on modifications of these operators in King’s sense, examining the rate of convergence for basic and modified operators. The prese...

In this paper we study approximation properties of exponential-type operators for functions from exponential weighted spaces. We focus on some modifications of these operators and we derive a new example of such operators. A probabilistic approach fo...

Several papers, mainly written by J. de la Call and co-authors, contain modifications of classical sequences of positive linear operators to obtain new sequences converging to limits which are not necessarily the identity operator. Such results were...

This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exp...

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval $[0,\infty )$. The operators act on exponential weighted spaces and a...

The concept of convexity is fundamental in order to produce various types of inequalities. Thus, convexity and integral inequality are closely related. The objectives of this paper are to present a new class of up and down convex fuzzy number valued...

In this paper, we use two new fractional integral operators with exponential kernel about the midpoint of the interval to construct some Hermite–Hadamard type fractional integral inequalities for h-convex functions. Taking two integral identiti...

The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional...

As an extension of an intuitionistic fuzzy set, a single-valued neutrosophic set is described independently by the membership functions of its truth, indeterminacy, and falsity, which is a subclass of a neutrosophic set (NS). However, in existing exp...

In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interva...

Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. M...

We examine a Szász–Mirakyan–Durrmeyer type operator that reproduces the functions 1 and $e^{2ax}$ for a fixed parameter $a>0.$ While its exponential reproduction property has been described in the classical literature, the effect of ex...

This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially $(\alpha ,h-m)-p$-convexity is utilized frequently. In addition, a fracti...

In this work, we construct a new class of Appell-type polynomials generated through extended truncated and truncated exponential kernels, and we analyze their core algebraic and operational features. In particular, we establish a suitable recurrence...

This article deals with analysing the positivity, monotonicity and convexity of the discrete nabla fractional operators with exponential kernels from the sense of Riemann and Caputo operators. These operators are called discrete nabla Caputo–Fa...

In this research, novel M-truncated fractional derivatives with three orders have been proposed. These operators involve truncated Mittag–Leffler function to generalize the Khalil conformable derivative as well as the M-derivative. The new oper...

This paper investigates a new class of fractional integral operators, namely, the exponentially damped Riesz-type operators within the framework of variable exponent Lebesgue spaces $L^{\mathtt{p}(·)}$. To the best of our knowledge, the boundedness of such...

The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces. Assuming that the evolution operat...

We present three new approximation properties of the Balázs–Szabados operators. Firstly, we prove that, in certain cases, these operators approximate some super-exponential functions on compact intervals. Next, we provide a new estimate of the error...

This paper presents a novel class of conformable integro-differential operators designed to model systems with rapid and ultra-rapid dynamics. This class of local operators enables the design of controllers and observers that induce hyperexponential...

Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered...

This paper develops a two-variable truncated-exponential-based Hahn–Appell polynomial family of order r in quantum q-calculus, generated by $\mathcal{A}\left(t\right){(1-\eta t^r)}^{-1}{e}_q^{wt}\left(\zeta t\right)$, where $\mathcal{A}\left(t\right)$ is a normalized determining function and $e_q^{wt}$ den...

In this paper, we define the $(p,q)$ -variant of Szász–Kantorovich operators via Dunkl-type generalization generated by an exponential function and study the Korovkin-type results. We also obtain the convergence of our operators...

This survey highlights the significant role of exponential operators and the monomiality principle in the theory of special polynomials. Using operational calculus formalism, we revisited classical and current results corresponding to a broad class o...

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to m...

The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. The case of electric circuits, ruled by non-integer derivatives or capacitors wit...

In UAV target localization, the accuracy of time delay estimation is the key to high-precision positioning. However, under low signal-to-noise ratio (SNR), time delay estimation suffers from serious secondary peak interference and low accuracy, which...

This article introduces $(p,q)$-analogs of the gamma integral operator and discusses their expansion to power functions, $(p,q)$-exponential functions, and $(p,q)$-trigonometric functions. Additionally, it validates other findings concerning $(p,q)$-analogs...

Regenerative chatter is an unfavorable phenomenon that severely affects machining efficiency and surface finish in milling operations. The prediction of chatter stability is an important way to obtain the stable cutting zone. Based on implicit multis...

One-dimensional equations of telegrapher’s-type (TE) and Guyer–Krumhansl-type (GK-type) with substantial derivative considered and operational solutions to them are given. The role of the exponential differential operators is discussed. T...

In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar...

Convex functions are studied very frequently by means of the Hadamard inequality. A symmetric function leads to the generalization of the Hadamard inequality; the Fejér–Hadamard inequality is one of the generalizations of the Hadamard in...

An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree $T=(\mathcal{V},\mathcal{E})$ with the natural distance d defined on graphs and a weighted measure $\mu$ of exponential g...

In 1915, Ramanujan stated the following formula ${\int }_0^{\infty }{t}^{x-1}\frac{{(-at;q)}_{\infty }}{{(-t;q)}_{\infty }}dt=\frac{\pi }{sin\pi x}\frac{{(q^{1-x},a;q)}_{\infty }}{{(q,a{q}^{-x};q}_{}}$...

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer...

The time-fractional Cattaneo equation is an equation where the fractional order $\alpha \in (1,2)$ has the capacity to model the anomalous dynamics of physical diffusion processes. In this paper, we consider an efficient scheme for solving such an eq...

We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator A in a complex Hilbert space as well as of the collection ${\left\{e^{tA}\right\}}_{t\ge 0}$ of its exponentials, which, under a certain co...

Earth data is essential for global environmental studies. Many Earth data types are naturally modeled by multidimensional arrays (tensors). Array (Tensor) DBMSs strive to be the best systems for tensor-related workloads and can be especially helpful...

In this review paper, our aim is to study the current research progress of q-difference equations for generalized Al-Salam–Carlitz polynomials related to theta functions and to give an extension of q-difference equations for q-exponential opera...

Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we esta...

Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instabili...

Time–space fractional diffusion equations are widely used to model anomalous transport in heterogeneous biological tissues, where memory effects, spatial nonlocality, and coefficient variability are intrinsically coupled. However, existing nume...

This study addresses the challenge of aligning inventory forecasting with sustainability and service level goals in re-order point systems. It introduces a semiparametric forecasting method based on exponential smoothing and M-estimation, designed to...

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence...

This study proposes an L1 discretization scheme (an accurate second-order finite difference method) for time-fractional diffusion equations involving the Caputo-type Erdélyi–Kober operator, which models anomalous diffusion. Our key contr...

In this article, the performance of brass electrode was investigated in a Zn-air (charcoal-based cathode) rechargeable battery. The construction of the battery was carried out with biodegradable materials, namely a cotton cloth diaphragm and carboxym...

The accurate forecasting of solar power generation is becoming increasingly important in the context of renewable energy integration and intelligent energy management. The variability of solar radiation, caused by changing meteorological conditions a...

The present study aims at investigating some characterizations of a new subclass $G_{\alpha }(\mu ,\tau )$ and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to...

This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of...

This paper’s main goal is to introduce left and right exponential trigonometric convex interval-valued mappings and to go over some of their important characteristics. Additionally, we demonstrate the Hermite–Hadamard inequality for inter...