一类分数阶非线性微分包含初值问题的可解性

在新的分数阶导数定义下,运用Bohnenblust-Karlin不动点定理并结合上下解方法研究了一类分数阶非线性微分包含初值问题{x~((α))(t)∈F(t,x(t)),t∈J=[a,b],a0,x(a)=x_0的可解性.其中,F:J×R→2~R是一个L~1-Carathéodary函数,x~((α))(t)表示x在t上的α阶导数,α∈(0,1].最后,分别给出了当集值映射F关于第二变量x次线性和至多线性增长时解的存在结果.

The solvability of Cauchy problem for nonlinear fractional differential inclusions

In this paper, using Bohnenblust-Karlin's fixed point theorem and combining the upper and lower solution method, we mainly study the solvability of Cauchy problem for nonlinear fractional differential inclusions  where F:J×R→2^R is L¹-Carathéodary function, x^(α)(t) denotes the conformable fractional derivative of x at t of order α, α∈(0,1]. By applying this theorem, we arrive at two existence results when the multi-valued nonlinearity F has sub-linear or linear growth about the second variable.