Fractional differential equations and inclusions with semiperiodic and three-point boundary conditions

Boundary value problems

Ravi P Agarwal¹  Ahmed Alsaedi²  Bashir Ahmad³ 

[1] Department of Mathematics, Texas A&M University, Kingsville, USA;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;    semi-periodic;    three-point;    boundary conditions;    existence;    fixed point;    34A08;    34A60;    34B15;   

DOI  :  10.1186/s13661-016-0533-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we investigate the existence of solutions for boundary value problems of fractional differential equations and inclusions with semiperiodic and three-point boundary conditions. The existence results for equations are obtained by applying Banach’s contraction mapping principle, Schaefer-type fixed point theorem, Leray-Schauder degree theory, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative, whereas the existence of solutions for convex and nonconvex set-valued maps (inclusion case) is shown via nonlinear alternative of Leray-Schauder type for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions, respectively. We emphasize that a variety of fixed point theorems are used to obtain different existence criteria for the problems at hand. Several examples are discussed for illustration of the obtained results. Moreover, an interesting observation related to symmetric second-order three-point boundary value problems is presented.

【 授权许可】

CC BY