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

被引：33
|
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.
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页数：10
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