一致分数阶时滞微分方程边值问题解的存在性与唯一性

Existence and Uniqueness of Solutions for Boundary Value Problems of Conformable Fractional Delay Differential Equations

用Leray-Schauder度理论和Banach压缩映射原理研究一致分数阶时滞微分方程边值问题{D^(β)_(0)+u(t)=f(t,u(t-τ)),t∈[0,1],u(t)=φ(t),t∈[-τ,0],u(0)+u′(0)=0,u(1)+u′(1)=0解的存在性与唯一性.在非线性项满足增长性条件和Lipschitz条件下,分别得到了该边值问题解的存在性与唯一性结果,并举例说明所得结果的适用性.

By using Leray-Schauder degree theory and Banach contraction mapping principle,we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations {D^(β)_(0)+u(t)=f(t,u(t-τ)),t∈[0,1],u(t)=φ(t),t∈[-τ,0],u(0)+u′(0)=0,u(1)+u′(1)=0,when the nonlinear term satisfied the growth condition and the Lipschitz condition,we obtained the results of existence and uniqueness of solution for the boundary value problem respectively,and gave an example to illustrate the applicability of the obtained results.