Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives

被引：1

作者：

Saber, Hicham ^{[1
]}

Ali, Arshad ^{[2
]}

Aldwoah, Khaled ^{[3
]}

Alraqad, Tariq ^{[1
]}

Moumen, Abdelkader ^{[1
]}

Alsulami, Amer ^{[4
]}

Eljaneid, Nidal ^{[5
]}

机构：

[1] Univ Hail, Coll Sci, Dept Math, Hail 55473, Saudi Arabia

[2] Univ Malakand, Dept Math, Chakdara 18000, Khyber Pakhtunk, Pakistan

[3] Islamic Univ Madinah, Fac Sci, Dept Math, Madinah 42351, Saudi Arabia

[4] Taif Univ, Turabah Univ Coll, Dept Math, Taif 21944, Saudi Arabia

[5] Univ Tabuk, Fac Sci, Dept Math, POB 741, Tabuk 71491, Saudi Arabia

来源：

FRACTAL AND FRACTIONAL | 2025年 / 9卷 / 02期

关键词：

impulsive and integral boundary conditions; fractional piecewise derivatives; nonlinear methods; variable kernel; discrete delay differential equations; existence and stability results; NUMERICAL-METHOD; EXISTENCE; MECHANICS; EQUATIONS;

D O I：

10.3390/fractalfract9020105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates a general class of variable-kernel discrete delay differential equations (DDDEs) with integral boundary conditions and impulsive effects, analyzed using Caputo piecewise derivatives. We establish results for the existence and uniqueness of solutions, as well as their stability. The existence of at least one solution is proven using Schaefer's fixed-point theorem, while uniqueness is established via Banach's fixed-point theorem. Stability is examined through the lens of Ulam-Hyers (U-H) stability. Finally, we illustrate the application of our theoretical findings with a numerical example.

引用

页数：19

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