The Langevin Equation in Terms of Generalized Liouville-Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral

被引：37

作者：

Ahmad, Bashir ^{[1
]}

Alghanmi, Madeaha ^{[1
]}

Alsaedi, Ahmed ^{[1
]}

Srivastava, Hari M. ^{[2
,3
]}

Ntouyas, Sotiris K. ^{[1
,4
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

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

[4] Univ Ioannina, Dept Math, Ioannina 45110, Greece

来源：

MATHEMATICS | 2019年 / 7卷 / 06期

关键词：

Langevin equation; generalized fractional integral; generalized Liouville-Caputo derivative; nonlocal boundary conditions; existence; fixed point;

D O I：

10.3390/math7060533

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary conditions involving a generalized integral operator. The modern techniques of functional analysis are employed to obtain the desired results. The paper concludes with illustrative examples.

引用

页数：10

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