On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives

被引：25

作者：

Abdeljawad, Thabet ^{[1
,2
]}

Madjidi, Fadila ^{[3
]}

Jarad, Fahd ^{[4
]}

Sene, Ndolane ^{[5
]}

机构：

[1] Prince Sultan Univ, Dept Math & Gen Sci, POB 66833, Riyadh 11586, Saudi Arabia

[2] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[3] Univ Mohamed Boudiaf, Dept Math, PB 166, Msila 28000, Algeria

[4] Cankaya Univ, Dept Math, TR-06790 Ankara, Turkey

[5] Univ Cheikh Anta Diop Dakar, Fac Sci Econom & Gest, Dept Math Decis, Lab Lmdan, BP 5683, Dakar, Senegal

来源：

MATHEMATICS | 2019年 / 7卷 / 10期

关键词：

generalized fractional operators; Mittag-Leffler bound; Mittag-Leffler stability; STABILITY ANALYSIS; THEOREM;

D O I：

10.3390/math7100946

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.

引用

页数：13

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