368 Results Found

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral...

In this paper, we introduce and investigate a new subclass of analytic functions in the open unit disk by combining the $(\lambda ,q)$-fractional differintegral operator with the Euler generating function through the technique of subordination. This cl...

This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to di...

In this paper, we introduce and study a Szász-type family of positive linear operators generated by Euler polynomials of negative order on $[0,\infty )$. The construction is based on an explicit finite representation of these polynomials with no...

This paper introduces a new family of extended degenerate Bell-based Appell polynomials by applying Euler’s integral as a fractional operator to the Appell-type degenerate Bell polynomials. Beginning with the exponential operational rule and em...

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices for fractional integration, we try to solve those system...

The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is a...

This paper investigates the significance of generating expressions, operational principles, and defining characteristics in the study and development of special polynomials. The focus is on a novel generalized family of degenerate 2D Appell polynomia...

In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations. The degenerate B...

The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by the author. Many properties of this operator are given. Using this operator, two new classes of special polynomi...

In this paper, we introduce and systematically study a new two-parameter family of affine $(q,\eta )$-Gould–Hopper-based Appell polynomials. These polynomials arise by fusing the affine $(q,\eta )$-exponential Gould–Hopper kernel with an inve...

First, we develop a direct operator method for solving boundary value problems for a class of nth order linear Volterra–Fredholm integro-differential equations of convolution type. The proposed technique is based on the assumption that the Volt...

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several...

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated wit...

This paper presents an innovative numerical method for solving two-dimensional weakly singular Volterra integral equations, including fractional Volterra integral equations with weak singularities. Solving these equations in higher dimensions and in...

Recent developments have shown that the widely used simplified differential model of Eringen’s nonlocal elasticity in nanobeam analysis is not equivalent to the corresponding and initially proposed integral models, the pure integral model and t...

There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that exp...

In this paper, we introduce and study Hermite–Kampé de Fériet Hahn–Appell polynomial sequences (HKdF Hahn–Appell sequences) within the unified framework of the Hahn difference operator. We establish three equivalent ch...

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction opera...

We study an Eulerian pantograph equation with proportional delay by means of a logarithmic change of variables, which transforms the problem into a constant-shift equation on the half-line. The main object is the maximal left-transport realization on...

To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of mic...

This paper investigates the temporal evolution of high-speed compressible fluids governed by the two-dimensional Euler equations in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into...

This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by t...

The population balance equations (PBEs) serve as the primary governing equations for simulating the crystallization process. Two-dimensional (2D) PBEs pertain to crystals that exhibit anisotropic growth, which is characterized by changes in two inter...

The explicit Euler method is widely used for the numerical integration of ordinary differential equations due to its simplicity and low computational cost; however, its accuracy and long-term qualitative behavior deteriorate for nonlinear oscillatory...

This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence a...

The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set $C^1[a,b]$, must satisfy. The Lagrange function depends on a generalized fractional derivative, on a g...

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and $\pi$ , a...

The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of p...

Semi-prime factorization is an increasingly important number theoretic problem, since it is computationally intractable. Further, this property has been applied in public-key cryptography, such as the Rivest–Shamir–Adleman (RSA) encryption systems fo...

We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on ${\mathbb{Z}}_p$ and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on ${\mathbb{Z}}_p$ of the two va...

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...

In this paper, we establish a new hybrid class of special polynomials, the Gould–Hopper–Fubini-based Appell polynomials. Using the monomiality principle, we derive their generating function and explore related properties and identities. W...

This work describes an innovative three-dimensional model of a proton exchange membrane electrolyzer. For the first time, a multi-phase model has captured segregated channel flow together with multiphase flow in a porous medium, as well as heat trans...

In this paper, we introduce and investigate a new class of analytic functions generated by Euler polynomials through a suitable normalization. Using classical tools from geometric function theory, including coefficient monotonicity, Fejér-type...

This research presents a fractional-order formulation and mathematical analysis of the Rössler chaotic attractor. By utilizing the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense, the classical integer-...

The goal of this article is to establish several new formulas and new results related to the Marichev-Saigo-Maeda fractional integral and fractional derivative operators which are applied on the $(p,q)$-extended Bessel function. The results are express...

The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline soluti...

This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved M...

In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in ear...

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leff...

We establish a new inequality of Hilbert-type containing positive homogeneous kernel ${(\min \{m,n\})}^{\lambda }$ and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the o...

In this study, we obtain new Hermite–Hadamard type inequalities involving an extended form of the Atangana–Baleanu fractional integral operator having Mittag-Leffler kernels. The approach is based on a suitable integral identity for diffe...

Our goal is to prove the Euler–Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler–Maclaurin summation formula will be considered for the case of functions of the class $C^{2k}\left([a,b]\right)$. A stronger version of the e...

Historic masonry towers are all around the world and play a significant role in shaping our built environment. Due to their slender shape, these towers are particularly vulnerable, as recent earthquakes have demonstrated. Many researchers have studie...

Attitude error models play an important role in analyzing the characteristics of navigation error propagation for the design and operation of strapdown inertial navigation systems (SINS). However, the majority of existing attitude error models focus...

The main result of this paper is a matched-pair decomposition of the space of symmetric contravariant tensors $\mathfrak{T}\mathcal{Q}$. From this procedure two complementary Lie subalgebras of $\mathfrak{T}\mathcal{Q}$ under mutual interaction arise. Introducing a lift operator, the matched pai...

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler’s identity, and Dedekind zeta functions of quadratic imaginary field...

Compound parabolic concentrator (CPC) photocatalytic reactors are commonly used for photocatalytic water splitting in hydrogen production. This study aimed to gain a better understanding of the physical processes in CPC photocatalytic reactors and pr...

This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating f...