A numerical comparative study of generalized Bernstein-Kantorovich operators

Kadak, Uğur; Özger, Faruk

doi:10.3934/mfc.2021021

Cited by 13 publications

(3 citation statements)

References 43 publications

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“…For further studies, one can also investigate (i) some substantially general forms of the Riemann-Liouville fractional integrals [27,28]; (ii) collocation methods based upon various orthogonal polynomials [11,14,26,29]; (iii) Volterra and related integro-differential equations [4]. Our next aim is to combine rational Chebyshev functions with approximation theory [13,19,20] to solve fractional integral equation.…”

Section: Discussionmentioning

confidence: 99%

Numerical solution of fractional Volterra integral equations based on rational Chebyshev approximation

Deniz,

Özger,

Özger

et al. 2023

MMN

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We aim to give the numerical method for solving the fractional Volterra integral equations of first and second kinds. We here use the techniques based upon rational Chebyshev functions and Riemann-Liouville fractional integrals. Some illustrative experiments with a view of estimating error and graphics are given in order to show the validity and applicability of the technique. Our experiments show that the new technique has high accuracy and is very efficient when compare to the other approaches existing in literature.

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Section: Discussionmentioning

confidence: 99%

Numerical solution of fractional Volterra integral equations based on rational Chebyshev approximation

Deniz,

Özger,

Özger

et al. 2023

MMN

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“…p,λ operators are provided. First, the needed standard notions and notations that were also given in the papers [33,34] are provided. Definition 1.…”

Section: Statistical Convergence Of Univariate Blending (α λ S)-berns...mentioning

confidence: 99%

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

et al. 2022

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This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A-statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters α and λ, and they propose better approximation results.

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“…In this section, we apply the BKS operator to the manipulator and obtain the recursive relationship of BKS polynomial according to the Bernstein polynomial [ 27 ]. Then, some properties of the BKS operator applied to the robotic manipulator controller are given according to the above-derived model.…”

Section: Model Derivation and Control Objectivesmentioning

confidence: 99%

A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator

Zhang

Wang

2022

Micromachines

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With the development of intelligent manufacturing and mechatronics, robotic manipulators are used more widely. There are complex noises and external disturbances in many application cases that affect the control accuracy of the manipulator servo system. On the basis of previous research, this paper improves the manipulator controller, introduces the Bernstein–Kantorovich–Stancu (BKS) operator, and proposes a modified robotic manipulator controller to improve the error tracking accuracy of the manipulator controller when observing complex disturbances and noises. In addition, in order to solve the problem that the coupling between the external disturbances of each axis of the manipulator leads to a large amount of computation when observing disturbances, an improved full-order observer is designed, which simplifies the parameters of the controller combined with the BKS operator and reduces the complexity of the algorithm. Through a theoretical analysis and a simulation test, it was verified that the proposed manipulator controller could effectively suppress external disturbance and noise, and the application of the BKS operator in the manipulator servo system control is feasible and effective.

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A numerical comparative study of generalized Bernstein-Kantorovich operators

Cited by 13 publications

References 43 publications

Numerical solution of fractional Volterra integral equations based on rational Chebyshev approximation

Numerical solution of fractional Volterra integral equations based on rational Chebyshev approximation

Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator

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