一类分数阶微分方程非奇次边值问题正解的存在性(英文)

Existence of Positive Solutions to a Class of Nonhomogeneous Boundary Value Problem of Fractional Differential Equation

考虑非线性分数阶微分方程非奇次边值问题正解的存在性:■,其中1<α2,0γ1,αγ+1是两个实数,Dα0+是标准的Riemann-Liouville微分,且f:[0,1]×[0,∞)→[0,∞)是连续函数.应用Leray-Schauder非线性选择定理和Banach不动点,获得了分数阶微分方程非奇次边值问题存在正解一些充分条件.作为应用,我们给出了几个例子并应用我们的定理证明了这些方程存在正解.

In this paper, we are concerned with the existence of nonhomogeneous boundary value problem positive solutions of nonlinear fractional differential equation ： D^α_0＋u（t）＋f（t,u（t））=0, 0〈t〈1, u（0）=0,D^γ_0＋u（t）｜i=1=b where 1 〈 α≤2,0 ≤γ ≤1 ,α ≥ γ ＋ 1 are two real numbers, D^α_0＋ is the standard Riemann- Liouville differentiation, and f： [0, 1 ]× [0, ∞） →[0, ∞ ） is a continuous function. By using nonlinear alternative of Leray - Schauder type and Banaeh fixed point theo- rem, some suffcient conditions ensuring the existence of positive solution are established for nonhomogeneous boundary value problem of fractional differential equation. As an application, some examples are given to illustrate our results.