带有p(t)-Laplacian和Erdélyi-Kober算子的分数阶边值问题的正解  

Positive Solutions for a Boundary Value Problem with p(t)-Laplacian and Erdélyi-Kober Operators

作　　者：薛亮 XUE Liang(Department of Basic Courses,Anhui Industrial Polytechnic College,Tongling 244000,China)

机构地区：[1]安徽工业职业技术学院基础部,安徽铜陵244000

出　　处：《湖州师范学院学报》2023年第10期1-6,共6页Journal of Huzhou University

基　　金：国家自然科学基金项目(11601048).

摘　　要：研究一类带有p(t)-Laplacian和Erdélyi-Kober积分算子的分数阶微分方程边值问题.首先,将该问题转化为对应的Hammerstein型积分方程;然后,在合适的工作空间构造算子方程,并在非线性项一些合适的条件下,利用不动点定理研究该算子方程不动点的存在性,从而获得原问题正解的存在性;最后,举例说明该结论的有效性.所得结论推广了该领域已有的一些研究成果.In this paper,we study the boundary value problems for a class of Caputo fractional differential equations involving p(t)-Laplacian operator and Erdélyi- Kober fractional integral operator.We first transform the problem into the corresponding Hammerstein-type integral equation,and then establish an operator equation under an appropriate work space.By applying the fixed point theorems,we study the existence of fixed points for the operator equation under some appropriate conditions for our nonlinearity,and then obtain the positive solutions for the original problem.Finally,an example is provided to illustrate our main result.The conclusions here extend the existing study.

关 键 词：分数阶微分方程 边值问题 不动点定理 正解 

分 类 号：O175.1[理学—数学] O175.8[理学—基础数学]