分数阶时滞微分方程正解的存在性

Existence of positive solutions of nonlinear fractional differential equations with delay

研究了一类非线性分数阶时滞微分方程L(D)[x(t)-x(0)]=f(t,xt),x(t)=φ(t)≥0,0t∈<[t-≤r,T0],正解的存在性和惟一性.在f(t,.)非减的条件下,通过运用上下解的方法,获得了该方程正解存在的充分条件,并利用Banach不动点定理证明了该方程正解的惟一性.

The existence and uniqueness of positive solutions for a class of nonlinear fractional differential equation with delay {L（D）[x（t）-x（0）3-f（t,xl）,0〈t≤T, x（t）=9（t）≥0,t∈[-r,0] is investigated. By using the sub and super-solution method, some suffcient conditions for its existence of positive solutions are obtained under the condition that f（t, ~ ） is nondecreasing, and the uniqueness of a positive solution is showed by application of the Banach fixed point theorem.