Approximation of durrmeyer type operators depending on certain parameters

Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper

Statistical convergence of Bernstein operators

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the statistical convergence of sequence of Bernstein polynomials. In this paper, we introduce the concepts of statistical convergence of Bernstein polynomials and VB−summability and related theorems. We also study Korovkin type-convergence of Bernstein polynomials

Identities Involving Some New Special Polynomials Arising from the Applications of Fractional Calculus

Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making use of the Caputo-fractional derivative, we derive some new interesting identities of these polynomials. It turns out that some known results are derived as special cases

A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hilbert space. Moreover, we make use of the theory of reproducing kernels to establish certain reproducing kernel functions in the aforementioned reproducing kernel Hilbert space. Furthermore, we give an approximation to the time-fractional derivative term by applying the finite difference scheme by our proposed method. Over and above, we present an appropriate technique to derive the numerical solution of the given equation by utilizing a pseudo-spectral method based on the reproducing kernel. Then, we provide two numerical examples to support the accuracy and efficiency of our proposed method. Finally, we apply numerical experiments to calculate the quality of our approximation by employing discrete error norms. © 2022, The Author(s)

A new class of partially degenerate Hermite-Genocchi polynomials

In this paper, firstly we introduce not only partially degenerate Hermite-Genocchi polynomials, but also a new generalization of degenerate Hermite-Genocchi polynomials. Secondly, we investigate some behaviors of these polynomials. Furthermore, we establish some implicit summation formulae and symmetry identities by making use of the generating function of partially degenerate Hermite-Genocchi polynomials. Finally, some results obtained here extend well-known summations and identities which we stated in the paper

A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator

Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. © 2022, The Author(s)

Construction of Degenerate qq-Daehee Polynomials with Weight α\alpha and its Applications

The fundamental aim of the present paper is to deal with introducing a new family of Daeheepolynomials which is called degenerate q-Daehee polynomials with weight α by usingp-adic q-integral on Zp. From this definition, we obtain some new summation formulaeand properties. We also introduce the degenerate q-Daehee polynomials of higher orderwith weight α and obtain some new interesting identities

Construction of Degenerate q-Daehee Polynomials with Weight α and its Applications

The fundamental aim of the present paper is to deal with introducing a new family of Daeheepolynomials which is called degenerate q-Daehee polynomials with weight α by usingp-adic q-integral on Zp. From this definition, we obtain some new summation formulaeand properties. We also introduce the degenerate q-Daehee polynomials of higher orderwith weight α and obtain some new interesting identities

Existence and multiplicity of positive solutions for boundary-value problems of non-linear fractional differential equations

The positive solutions under particular boundary circumstances arising from non-linear fractional differential equations were recently constructed [S. Zhang, Positive. Solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differ. Eq., Vol. 2006, 36, 1-12, 2006]. In this paper, we also discuss the existence and multiplicity of positive solutions for the following nonlinear fractional differential equation boundaryvalue problem (Equation Presented) where 2 < ? ? 3 is a real number, and D?0+ is the Caputo's fractional derivative, and f: [0,1] × [0,+?) ? [0,+?) is continuous. By using Krasnoesel'skii's fixed-point theorem on cones, we obtain various results on the existence of positive solutions of the boundary-value problem

Computation of eigenvalues and fundamental solutions of a fourth-order boundary value problem

In this work, we study a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. We discuss asymptotic behavior of its eigenvalues and fundamental solutions