2,785 Results Found

Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Ja...

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigat...

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequ...

In this article, for the first time by using Caputo-type fractional derivatives, we introduce three new subclasses of bi-univalent functions associated with bounded boundary rotation in an open unit disk to obtain non-sharp estimates of the first two...

Macrophages play a crucial role in regulating immune responses, inflammation, and tissue repair. Depending on environmental cues, they polarize into pro-inflammatory M1 or anti-inflammatory, pro-regenerative M2 phenotypes. Extracellular vesicles (EVs...

A geometrical formulation of estimation theory for finite-dimensional $C^{\ast }$-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer&ndas...

In this article, through the application of the q-Sălăgean operator associated with functions characterized by bounded boundary rotation, we propose a few new subclasses of bi-univalent functions that utilize the q-Sălăgean operat...

We study a class of conformable time-fractional stochastic equation $T_{\alpha ,t}^{a}u(x,t)=\sigma \left(u(x,t)\right){\dot{W}}_t,x\in \mathbb{R},t\in [a,T],T<\infty ,0<\alpha <1.$ The initial con...

In this paper, we discussed a new subclass ${\mathcal{J}\mathcal{Q}}_{⅁,A}^B\left(q\right)$ of bi-univalent functions in the unit disk $\mathbb{U}$ using q-generalized Janowski function and q-derivative. Additionally, certain properties were examined and effectively demonstrated, such as the s...

Polycyclic aromatic hydrocarbons (PAHs) and their derivatives have received extensive attention due to their negative effects on the environment and on human health. However, few studies have performed comprehensive assessments of PAHs emitted from p...

In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of t...

We establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a,b)$, and the fractional bounded variation spaces of f...

In this article, we begin by introducing two classes of lacunary fractional spline functions by using the Liouville–Caputo fractional Taylor expansion. We then introduce a new higher-order lacunary fractional spline method. We not only derive the exi...

Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and conside...

This paper studies a fractional differential equation combined with a Liouville–Caputo fractional differential operator, namely, ${}^{LC}{\mathcal{D}}_{\eta }^{\beta ,\gamma }Q\left(t\right)=\lambda \vartheta (t,Q\left(t\right)),t\in [c,d],\beta ,\gamma \in (0,1],\eta \in [0,1],$ wher...

The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, a...

It is well established that financial development and innovation promote economic growth through improving the allocation of capital, enhancing risk management, contributing to price discovery, and increasing market efficiencies. While a vast empiric...

The structure and interactions of several aminopropyl–azithromycin derivatives (1a–c) have been studied by using NMR spectroscopy and docking calculations. Compounds 1a–c are precursors in the synthesis of macrozones, novel bioactive azithromycin–thi...

In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In...

In the present work, the numerical solution of fractional delay integro-differential equations (FDIDEs) with weakly singular kernels is addressed by designing a Vieta–Fibonacci collocation method. These equations play immense roles in scientifi...

Osteoarthritis (OA) is a degenerative joint disease with limited therapeutic options, where inflammation plays a critical role in disease progression. Extracellular vesicles (EV) derived from mesenchymal stromal cells (MSC) have shown potential as a...

The principal aim of this paper is to introduce the extended Voigt-type function ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and its counterpart extension ${\mathbb{W}}_{\mu ,\nu }(x,y)$, involving the Neumann function $Y_{\nu }$ in the kernel of the representing integral. The newly defined integra...

We show that the derivative of the relative entropy with respect to its parameters is lower and upper bounded. We characterize the conditions under which this derivative can reach zero. We use these results to explain when the minimum relative entrop...

Four new ligands and four new copper (II) coordination compounds were prepared and characterized by chemical, elemental analysis, cytotoxicity, and FTIR spectroscopy (Fourier transform infrared spectroscopy). The nature of metal–ligand coordination w...

In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier–Stokes equation. Such bounds are instructive in the numerical investigation of intermittency that is often observed in simul...

Chronic kidney disease (CKD) afflicts more than 500 million people worldwide and is one of the fastest growing global causes of mortality. When glomerular filtration rate begins to fall, uremic toxins accumulate in the serum and significantly increas...

In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are...

The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Non...

The protein family of small GTPases controls cellular processes by acting as a binary switch between an active and an inactive state. The most prominent family members are H-Ras, N-Ras, and K-Ras isoforms, which are highly related and frequently muta...

In the present article, we establish conditions for the asymptotic periodicity of bounded mild solutions in two distinct cases of evolution equations. The first class involves non-densely defined operators, while the second class incorporates densely...

In this paper, we present some Ostrowski–Grüss-type inequalities on time scales for functions whose derivatives are bounded by functions for k points via a parameter. The 2D versions of these inequalities are also presented. Our results ge...

In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator ${\mathcal{C}}_{\mathsf{ȷ}}^{\varrho }$, which encompasses and exten...

By using q-convolution, we determine the coefficient bounds for certain symmetric subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler-type differential equation of orde...

Scholars from several disciplines have recently expressed interest in the field of fractional q-calculus based on fractional integrals and derivative operators. This article mathematically applies the fractional q-differential and q-integral operator...

Acute kidney injury (AKI) is a frequent disease encountered in the hospital, with a higher incidence in intensive care units. Despite progress in renal replacement therapy, AKI is still associated with early and late complications, especially cardiov...

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients $\left|a_2\right|$ and $\left|a_3\right|$ for fu...

In this paper, by means of the second Chebyshev wavelet and its operational matrix, we solve a system of fractional-order Volterra–Fredholm integro-differential equations with weakly singular kernels. We estimate the functions by using the wavelet ba...

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients $\left|a_2\right|$ and $\left|a_3\right|$ for functio...

In this study, we present two novel subclasses of bi-univalent functions defined in the open unit disk, utilizing Liouville–Caputo fractional derivatives. We find constraints on initial Taylor coefficients $|c_2|$, $|c_3|$ for functions in these subc...

Hilbert-type inequalities derive from the classical Hilbert inequality, and their theoretical work has key applications not only in operator theory but also in various analytic disciplines. In this paper, we have achieved the parametric conditions re...

We consider a stochastic nonlinear fractional Langevin equation of two fractional orders $D^{\beta }(D^{\alpha }+\gamma )\psi \left(t\right)=\lambda \vartheta (t,\psi \left(t\right))\dot{w}\left(t\right),0<t\le 1.$ Given some suitable conditions on the above parameters, we prove the existence and uniqueness of the mild solution to the...

We defined two new subclasses of analytic bi-univalent function class $\Sigma ,$ in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients $|a_2|,|a_3|$ and $|a_4|$ for the functions...

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaini...

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines ${\mathcal{S}}_q^{\mathrm{\&d}}$...

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization ${\mathcal{R}}_q\left(h\right)$ of the class $\mathcal{R}\left(h\right)$ of analytic functions, which are associated with the leaf-like domain in the o...

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo’s frac...

The manuscript is an initiative to construct a full and exhaustive theory of analytical multivariate functions in any complete Reinhardt domain by introducing the concept of $\mathbf{L}$-index in joint variables for these functions for a given continuous, non-n...

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, exist...

This study presents a comprehensive analysis of the semilocal convergence properties of a high-order iterative scheme designed to solve nonlinear equations in Banach spaces. The investigation is carried out under the assumption that the first derivat...

In the present paper, the authors introduce and investigate two new subclasses of the function class $\mathcal{B}$ of bi-univalent analytic functions in an open unit disk $\mathcal{U}$ connected with a linear q-convolution operator. The bounds on the coefficients $|c_2|,|c_3|$...