Analysis of Cauchy problem with fractal-fractional differential operators

被引：3

作者：

Alharthi, Nadiyah Hussain ^{[3
]}

Atangana, Abdon ^{[1
,2
]}

Alkahtani, Badr S. ^{[4
]}

机构：

[1] Univ Free State, Inst Groundwater Studies, Fac Nat & Agr Sci, ZA-9300 Bloemfontein, South Africa

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

[3] Imam Mohammad Ibn Saud Islamic Univ, Dept Math & Stat, Coll Sci, POB 90950, Riyadh 11623, Saudi Arabia

[4] King Saud Univ, Coll Sci, Dept Math, POB 1142, Riyadh 11989, Saudi Arabia

来源：

DEMONSTRATIO MATHEMATICA | 2023年 / 56卷 / 01期

关键词：

fractal-fractional; power law; exponential decay; Mittag-Leffler function; numerical scheme; inequalities;

D O I：

10.1515/dema-2022-0181

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Cauchy problems with fractal-fractional differential operators with a power law, exponential decay, and the generalized Mittag-Leffler kernels are considered in this work. We start with deriving some important inequalities, and then by using the linear growth and Lipchitz conditions, we derive the conditions under which these equations admit unique solutions. A numerical scheme was suggested for each case to derive a numerical solution to the equation. Some examples of fractal-fractional differential equations were presented, and their exact solutions were obtained and compared with the used numerical scheme. A nonlinear case was considered and solved, and numerical solutions were presented graphically for different values of fractional orders and fractal dimensions.

引用

页数：15

共 17 条

[1] On Cauchy problem for fractional parabolic-elliptic Keller-Segel model [J].