Nonstandard finite difference method for solving complex-order fractional Burgers' equations

被引：15

作者：

Sweilam, N. H. ^{[1
]}

AL-Mekhlafi, S. M. ^{[2
]}

Baleanu, D. ^{[3
,4
]}

机构：

[1] Cairo Univ, Dept Math, Fac Sci, Giza, Egypt

[2] Sanaa Univ, Fac Educ, Dept Math, Sanaa, Yemen

[3] Cankaya Univ, Dept Math, Etimesgut, Turkey

[4] Inst Space Sci, Magurele, Romania

来源：

JOURNAL OF ADVANCED RESEARCH | 2020年 / 25卷

关键词：

Burgers' equations; Complex order fractional derivative; Nonstandard weighted average finite difference method; Stability analysis; NONLINEAR PDES; DERIVATIVES; CALCULUS; MODEL;

D O I：

10.1016/j.jare.2020.04.007

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers' equations. A new parameter sigma(t) is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter sigma(t) and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.

引用

页码：19 / 29

页数：11

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