k-Hankel Gabor Transform on $$\mathbb {R}^{d}$$ and Its Applications to the Reproducing Kernel Theory

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Hatem Mejjaoli
Keyword(s):  
Reproducing Kernel ◽  
Gabor Transform ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

scholarly journals Solving non-local fractical heat equations based on the reproducing kernel method

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 711-716
Author(s):  
Xiuying Li ◽  
Boying Wu
Keyword(s):  
Boundary Conditions ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Nonlocal Conditions ◽  
Heat Equations ◽  
Reproducing Kernel Method ◽  
Local Boundary ◽  
Non Local ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

In this paper, a numerical method is proposed for 1-D fractional heat equations subject to non-local boundary conditions. The reproducing kernel satisfying nonlocal conditions is constructed and reproducing kernel theory is applied to solve the considered problem. A numerical example is given to show the effectiveness of the method.

scholarly journals Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Er Gao ◽  
Songhe Song ◽  
Xinjian Zhang
Keyword(s):  
Reproducing Kernel ◽  
New Method ◽  
Universal Method ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Weighted Integral ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas.

scholarly journals Explicit Solution of Telegraph Equation Based on Reproducing Kernel Method

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Mustafa Inc ◽  
Ali Akgül ◽  
Adem Kiliçman
Keyword(s):  
Exact Solution ◽  
Explicit Solution ◽  
Reproducing Kernel ◽  
Initial Conditions ◽  
Kernel Method ◽  
Telegraph Equation ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

We propose a reproducing kernel method for solving the telegraph equation with initial conditions based on the reproducing kernel theory. The exact solution is represented in the form of series, and some numerical examples have been studied in order to demonstrate the validity and applicability of the technique. The method shows that the implement seems easy and produces accurate results.

Simulation of Signal Based on the Reproducing Kernel Spline

2012 ◽  
Vol 532-533 ◽  
pp. 1482-1486
Author(s):  
Xiao Jian Ma
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Reproducing Kernel ◽  
Approximation Property ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Boundary Extension ◽  
Signal Simulation ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

In signal processing, no matter the classical Fourier transform or the new wavelet transform is essentially related to kernel theory. The paper gives a reproducing kernel and its form is very simple. And by this kernel, the spline interpolation method can be constructed. Meanwhile, its best approximation property is proved. The numerical experiment results show that the interpolation method is convenient for numerical calculation and it has features of less calculation, higher approximation precision. Specially, the method has more advantages relative to Fourier analysis. That is, needless to prefilter and boundary extension, it can resolve ‘jumps’ at the edges in signal processing. And a new idea for signal simulation is put forward and the reproducing kernel theory is further enriched.

A New Numerical Method for Solving Nonlinear Fractional Fokker–Planck Differential Equations

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
BeiBei Guo ◽  
Wei Jiang ◽  
ChiPing Zhang
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Simple Algorithm ◽  
High Accuracy ◽  
Computational Work ◽  
Reproducing Kernel Theory ◽  
Transport Problems ◽  
Fokker Planck

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

scholarly journals A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mustafa Inc ◽  
Ali Akgül ◽  
Adem Kiliçman
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Kdv Equation ◽  
Reproducing Kernel Hilbert Space ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
The Kdv Equation ◽  
Novel Method ◽  
Reproducing Kernel Theory

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.

scholarly journals Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag-Leffler kernel differential operator

2021 ◽  
Author(s):  
omar abu arqub ◽  
Jagdev Singh ◽  
Banan Maayah ◽  
Mohammed Alhodaly
Keyword(s):  
Reproducing Kernel ◽  
Differential Operators ◽  
Numerical Solutions ◽  
Reproducing Kernel Hilbert Space ◽  
Research Work ◽  
Three Dimensional ◽  
Characterization Theorem ◽  
Space Technique ◽  
Kernel Approach ◽  
Reproducing Kernel Theory

In this research study, fuzzy fractional differential equations in presence of the Atangana-Baleanu-Caputo differential operators are analytically and numerically treated using extended reproducing Kernel Hilbert space technique. With the utilization of a fuzzy strongly generalized differentiability form, a new fuzzy characterization theorem beside two fuzzy fractional solutions is constructed and computed. To besetment the attitude of fuzzy fractional numerical solutions; analysis of convergence and conduct of error beyond the reproducing kernel theory are explored and debated. In this tendency, three computational algorithms and modern trends in terms of analytic and numerical solutions are propagated. Meanwhile, the dynamical characteristics and mechanical features of these fuzzy fractional solutions are demonstrated and studied during two applications via three-dimensional graphs and tabulated numerical values. In the end, highlights and future suggested research work are eluded.

Sign in / Sign up

Export Citation Format

Share Document