Analysis of a physically-relevant variable-order time-fractional reaction-diffusion model with Mittag-Leffler kernel

被引：7

作者：

Zheng, Xiangcheng ^{[1
]}

Wang, Hong ^{[1
]}

Fu, Hongfei ^{[2
]}

机构：

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2021年 / 112卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Fractional ordinary differential equation; Time-fractional reaction-diffusion equation; Mittag-Leffler kernel; Variable-order; Well-posedness; DERIVATIVES; EQUATIONS;

D O I：

10.1016/j.aml.2020.106804

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that the well-posedness of time-fractional reaction-diffusion models with Mittag-Leffler kernel usually requires non-physical constraints on the initial data. In this paper, we propose a variable-order time-fractional reaction-diffusion equation with Mittag-Leffler kernel and prove that the aforementioned constraints could be eliminated by imposing the integer limit of the variable fractional order at the initial time, which mathematically demonstrates the physically-relevance of the variable-order modifications. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：7

共 14 条

[11] Respiration Effect on Plankton-Oxygen Dynamics in view of non-singular time fractional derivatives [J].

Sekerci, Yadigar ;

Ozarslan, Ramazan .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2020, 553

[12] Fractional-order derivatives defined by continuous kernels are too restrictive [J].

Stynes, Martin .

APPLIED MATHEMATICS LETTERS, 2018, 85 :22-26

[13]

THOMEE V, 1984, LECT NOTES MATH, V1054, P1

[14] Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative [J].

Zheng, Xiangcheng ;

Wang, Hong ;

Fu, Hongfei .

CHAOS SOLITONS & FRACTALS, 2020, 138

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