Three-Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative

被引:20
|
作者
Wongcharoen, Athasit [1 ]
Ahmad, Bashir [2 ]
Ntouyas, Sotiris K. [2 ,3 ]
Tariboon, Jessada [4 ]
机构
[1] King Mongkuts Univ Technol North Bangkok, Dept Mech Engn Technol, Coll Ind Engn Technol, Bangkok 10800, Thailand
[2] King Abdulaziz Univ, Nonlinear Anal & Appl Math NAAM Res Grp, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia
[3] Univ Ioannina, Dept Math, Ioannina 45110, Greece
[4] King Mongkuts Univ Technol North Bangkok, Fac Sci Appl, Dept Math, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok 10800, Thailand
关键词
DIFFERENTIAL-EQUATIONS;
D O I
10.1155/2020/9606428
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach's fixed-point theorem to obtain the uniqueness result, while the nonlinear alternative of the Leray-Schauder type and Krasnoselskii's fixed-point theorem are applied to obtain the existence results for the single-valued problem. Existence results for the convex and nonconvex valued cases of the inclusion problem are derived via the nonlinear alternative for Kakutani's maps and Covitz and Nadler's fixed-point theorem respectively. Examples illustrating the obtained results are also constructed. (2010) Mathematics Subject Classifications. This study is classified under the following classification codes: 26A33; 34A08; 34A60; and 34B15.
引用
收藏
页数:11
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