吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
Journal of Jilin University (Science Edition)
2015年
5期
835-840
,共6页
分数阶微分方程%反周期边界条件%存在性%唯一性
分數階微分方程%反週期邊界條件%存在性%唯一性
분수계미분방정%반주기변계조건%존재성%유일성
fractional differential equation%anti-periodic boundary conditions%existence%uniqueness
考虑一个非线性项中含有关于未知函数的积分算子的非线性分数阶的反周期边值问题，其导数类型为 Caputo 型分数阶导数，阶数为2<α≤3.应用 Schauder 不动点定理和压缩映象原理证明了该问题解的存在性与唯一性.
攷慮一箇非線性項中含有關于未知函數的積分算子的非線性分數階的反週期邊值問題，其導數類型為 Caputo 型分數階導數，階數為2<α≤3.應用 Schauder 不動點定理和壓縮映象原理證明瞭該問題解的存在性與唯一性.
고필일개비선성항중함유관우미지함수적적분산자적비선성분수계적반주기변치문제，기도수류형위 Caputo 형분수계도수，계수위2<α≤3.응용 Schauder 불동점정리화압축영상원리증명료해문제해적존재성여유일성.
A nonlinear fractional anti-periodic boundary problem was considered, the differential operator of which is the Caputo sense of order 2<α≤3.The feature of this problem is that nonlinear term contains integral operators about unknown function.The existence and uniqueness of solution were proved via the Schauder fixed point theorem and the contraction mapping principle.
