scholarly journals The piecewise reproducing kernel method for the time variable fractional order advection-reaction-diffusion equations

2021 ◽  
pp. 21-21
Author(s):  
Dan-Dan Dai ◽  
Ting-Ting Ban ◽  
Yu-Lan Wang ◽  
Wei Zhang
Keyword(s):  
Fractional Order ◽  
Legendre Polynomials ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Reaction Diffusion ◽  
Time Variable ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Variable Order ◽  
Reproducing Kernel Method

This paper structures some new reproductive kernel spaces based on Legendre polynomials to solve time variable order fractional advection-reaction-diffusion equations. Some examples are given to show the effectiveness and reliability of the method.

scholarly journals The reproducing kernel for the reaction-diffusion model with a time variable fractional order

2020 ◽  
Vol 24 (4) ◽  
pp. 2553-2559 ◽  
Author(s):  
Wei Zhang ◽  
Yulan Wang ◽  
Meichun Wang
Keyword(s):  
Fractional Calculus ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Reaction Diffusion ◽  
Time Variable ◽  
Variable Order ◽  
Complex Reaction ◽  
Reproducing Kernel Method ◽  
Reaction Diffusion Model ◽  
Frame Work

The variable-order fractional calculus has become a useful mathematical frame-work to describe a complex reaction-diffusion process. It is very hard to solve the problem, and there is almost no analytical method available in open literature. In this article, the reproducing kernel method is proposed for this purpose, and some examples show that the method is of high precision.

scholarly journals Numerical Solution of a Class of Time-Fractional Order Diffusion Equations in a New Reproducing Kernel Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoli Zhang ◽  
Haolu Zhang ◽  
Lina Jia ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Diffusion Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces ◽  
Methods Numerical

In this paper, we structure some new reproducing kernel spaces based on Jacobi polynomial and give a numerical solution of a class of time fractional order diffusion equations using piecewise reproducing kernel method (RKM). Compared with other methods, numerical results show the reliability of the present method.

scholarly journals Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

2020 ◽  
Vol 4 (2) ◽  
pp. 27 ◽  
Author(s):  
Onur Saldır ◽  
Mehmet Giyas Sakar ◽  
Fevzi Erdogan
Keyword(s):  
Fractional Order ◽  
Reproducing Kernel ◽  
Burgers Equation ◽  
Kernel Method ◽  
Reproducing Kernel Hilbert Space ◽  
Neumann Boundary ◽  
Kernel Functions ◽  
Iterative Approach ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces

In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective.

Numerical treatment of fractional order Cauchy reaction diffusion equations

2017 ◽  
Vol 103 ◽  
pp. 578-587 ◽  
Author(s):  
Sajjad Ali ◽  
Samia Bushnaq ◽  
Kamal Shah ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Numerical Treatment
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