A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

M. Hosseininia; M. H. Heydari; Z. Avazzadeh; F. M. Maalek Ghaini

doi:10.1016/j.enganabound.2021.03.006

A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

M. Hosseininia, M. H. Heydari^*, Z. Avazzadeh, F. M. Maalek Ghaini

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation. An efficient and accurate hybrid method based on the shifted orthogonal Bernoulli polynomials and radial basis functions is developed for solving this equation. The presented method converts solving the problem under consideration into solving a system of algebraic equations. The applicability and accuracy of the proposed method are investigated by solving some numerical examples.

Original language	English
Pages (from-to)	18-28
Number of pages	11
Journal	Engineering Analysis with Boundary Elements
Volume	127
DOIs	https://doi.org/10.1016/j.enganabound.2021.03.006
Publication status	Published - 1 Jun 2021

Keywords

Heydari-Hosseininia fractional derivative
Orthogonal Bernoulli polynomials
Radial basis functions
Reaction-advection-diffusion equation

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10.1016/j.enganabound.2021.03.006

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Hosseininia, M., Heydari, M. H., Avazzadeh, Z., & Maalek Ghaini, F. M. (2021). A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation. Engineering Analysis with Boundary Elements, 127, 18-28. https://doi.org/10.1016/j.enganabound.2021.03.006

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title = "A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation",

abstract = "In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation. An efficient and accurate hybrid method based on the shifted orthogonal Bernoulli polynomials and radial basis functions is developed for solving this equation. The presented method converts solving the problem under consideration into solving a system of algebraic equations. The applicability and accuracy of the proposed method are investigated by solving some numerical examples.",

keywords = "Heydari-Hosseininia fractional derivative, Orthogonal Bernoulli polynomials, Radial basis functions, Reaction-advection-diffusion equation",

author = "M. Hosseininia and Heydari, {M. H.} and Z. Avazzadeh and {Maalek Ghaini}, {F. M.}",

note = "Publisher Copyright: {\textcopyright} 2021",

year = "2021",

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day = "1",

doi = "10.1016/j.enganabound.2021.03.006",

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AU - Hosseininia, M.

AU - Heydari, M. H.

AU - Avazzadeh, Z.

AU - Maalek Ghaini, F. M.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation. An efficient and accurate hybrid method based on the shifted orthogonal Bernoulli polynomials and radial basis functions is developed for solving this equation. The presented method converts solving the problem under consideration into solving a system of algebraic equations. The applicability and accuracy of the proposed method are investigated by solving some numerical examples.

AB - In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation. An efficient and accurate hybrid method based on the shifted orthogonal Bernoulli polynomials and radial basis functions is developed for solving this equation. The presented method converts solving the problem under consideration into solving a system of algebraic equations. The applicability and accuracy of the proposed method are investigated by solving some numerical examples.

KW - Heydari-Hosseininia fractional derivative

KW - Orthogonal Bernoulli polynomials

KW - Radial basis functions

KW - Reaction-advection-diffusion equation

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U2 - 10.1016/j.enganabound.2021.03.006

DO - 10.1016/j.enganabound.2021.03.006

M3 - Article

AN - SCOPUS:85103428152

SN - 0955-7997

VL - 127

SP - 18

EP - 28

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -

A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

Abstract

Keywords

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