A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives

被引：20

作者：

Baleanu, D. ^{[1
,2
]}

Alzabut, J. ^{[3
]}

Jonnalagadda, J. M. ^{[4
]}

Adjabi, Y. ^{[5
]}

Matar, M. M. ^{[6
]}

机构：

[1] Cankaya Univ, Dept Math, Ankara, Turkey

[2] Inst Space Sci, Magurele, Romania

[3] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia

[4] Birla Inst Technol & Sci Pilani, Dept Math, Hyderabad, India

[5] Univ Mhamed Bougara, Fac Sci, Dept Math, Boumerdes, Algeria

[6] Al Azhar Univ Gaza, Dept Math, Gaza, Palestine

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Non-singular fractional derivatives; Sturm-Liouville problem; Langevin equation; Fixed point theorems; Existence; Solutions dependence; Stability; EXISTENCE;

D O I：

10.1186/s13662-020-02690-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.

引用

页数：30

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