Analysis of nonlinear ordinary differential equations with the generalized Mittag-Leffler kernel

被引：1

作者：

Atangana, Abdon ^{[1
,2
]}

Mishra, Jyoti ^{[3
]}

机构：

[1] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, Bloemfontein, South Africa

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[3] Gyan Ganga Inst Technol & Sci, Dept Math, Jabalpur, Madhya Pradesh, India

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2023年 / 20卷 / 11期

关键词：

nonlinear equation; Picard iteration; Atangana-Baleanu derivative; Euler and Heun's approaches;

D O I：

10.3934/mbe.2023875

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The Picard iterative approach used in the paper to derive conditions under which nonlinear ordinary differential equations based on the derivative with the Mittag-Leffler kernel admit a unique solution. Using a simple Euler approximation and Heun's approach, we solved this nonlinear equation numerically. Some examples of a nonlinear linear differential equation were considered to present the existence and uniqueness of their solutions as well as their numerical solutions. A chaotic model was also considered to show the extension of this in the case of nonlinear systems.

引用

页码：19763 / 19780

页数：18

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