文章基本信息

标题：On solutions of a class of three-point fractional boundary value problems
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作者：Zhanbing Bai ; Yu Cheng ; Sujing Sun 等
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2020
卷号：2020
期号：1
页码：1-12
DOI：10.1186/s13661-019-01319-x
出版社：Hindawi Publishing Corporation
摘要：Existence results for the three-point fractional boundary value problem $$\begin{aligned}& D^{\alpha}x(t)= f \bigl(t, x(t), D^{\alpha-1} x(t) \bigr),\quad 0< t< 1, \\& x(0)=A, \qquad x(\eta)-x(1)=(\eta-1)B, \end{aligned}$$ are presented, where $A, B\in\mathbb{R}$, $0<\eta<1$, $1<\alpha\leq2$. $D^{\alpha}x(t)$ is the conformable fractional derivative, and $f: [0, 1]\times\mathbb{R}^{2}\to\mathbb{R}$ is continuous. The analysis is based on the nonlinear alternative of Leray–Schauder..
关键词：Boundary value problems ; Conformable fractional derivative ; Nonlinear alternative of Leray–Schauder ;