文章基本信息

标题：Extremal solutions for some periodic fractional differential equations
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作者：Wei Zhang ; Zhanbing Bai ; Sujing Sun 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：179
DOI：10.1186/s13662-016-0869-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：By using the lower and upper solution method, the existence of an iterative solution for a class of fractional periodic boundary value problems, D 0 + α u ( t ) = f ( t , u ( t ) ) , t ∈ ( 0 , h ) , lim t → 0 + t 1 − α u ( t ) = h 1 − α u ( h ) , $$\begin{aligned}& D_{0+}^{\alpha}u(t)=f\bigl(t, u(t)\bigr),\quad t \in(0, h),\\& \lim_{t \to0^{+}}t^{1-\alpha}u(t) = h^{1-\alpha}u(h), \end{aligned}$$ is discussed, where 0 < h < + ∞ $0< h<+\infty$ , f ∈ C ( [ 0 , h ] × R , R ) $f\in C([0, h]\times R, R)$ , D 0 + α u ( t ) $D_{0+}^{\alpha}u (t) $ is the Riemann-Liouville fractional derivative, 0 < α < 1 $0<\alpha< 1$ . Different from other well-known results, a new condition on the nonlinear term is given to guarantee the equivalence between the solution of the periodic boundary value problem and the fixed point of the corresponding operator. Moreover, the existence of extremal solutions for the problem is given.
关键词：fractional periodic boundary value problem ; extremal solution ; existence