Existence results for Langevin equations involving generalized Liouville-Caputo fractional derivatives with non-local boundary conditions

被引：0

作者：

Dhaniya, Sombir ^{[1
]}

Kumar, Anoop ^{[1
]}

Khan, Aziz ^{[2
]}

Abdeljawad, Thabet ^{[2
,3
,4
,5
]}

机构：

[1] Cent Univ Punjab, Dept Math & Stat, Bathinda 151401, Punjab, India

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

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

[4] Kyung Hee Univ, Dept Chem, 26 Kyungheedae Ro, Seoul 02447, South Korea

[5] Sefako Makgatho Hlth Sci Univ, Dept Math & Appl Math, ZA-0204 Garankuwa, Medusa, South Africa

来源：

ALEXANDRIA ENGINEERING JOURNAL | 2024年 / 90卷

关键词：

Liouville-Caputo generalized fractional; derivative (GFD); Langevin equation (LE); Krasonoselskii's fixed point theorem; Banach contraction mapping principle; Non-local boundary conditions; Generalized fractional operator; DYNAMICS;

D O I：

10.1016/j.aej.2024.01.025

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The main objective of the present paper is to establish the existence and uniqueness (EU) results for nonlinear fractional Langevin equation involving Liouville-Caputo generalized fractional derivative (GFD) of different order with non-local boundary conditions. The existence solution is obtained by using Krasnoselskii's fixed point theorem, and the uniqueness result is obtained by using the Banach contraction mapping principle. An example is introduced to validate the effectiveness of the results. The results are novel and provide an extension to some of the findings known in the literature.

引用

页码：153 / 160

页数：8

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