On the nonlocal Katugampola fractional integral conditions for fractional Langevin equation

Advances in Difference Equations

Chatthai Thaiprayoon¹  Sotiris K Ntouyas²  Jessada Tariboon³ 

[1] Department of Mathematics, Faculty of Science, Burapha University, Chonburi, Thailand;Department of Mathematics, University of Ioannina, Ioannina, Greece;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: fractional differential equations;    generalized fractional integral;    Katugampola fractional integral;    nonlocal boundary conditions;    fixed point theorems;    26A33;    34A08;   

DOI  :  10.1186/s13662-015-0712-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Riemann-Liouville type fractional derivatives with the nonlocal Katugampola fractional integral conditions. A variety of fixed point theorems are used such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder degree theory. Enlightening examples of the obtained results are also presented.

【 授权许可】

CC BY