一致分数阶导数下的微分方程边值问题多个正解的存在性

Existence of Multiple Positive Solutions for Boundary Value Problems of Differential Equations under Conformable Fractional Derivative

运用不动点指数理论,讨论了分数阶微分方程边值问题{u^(δ)(t)=f(t,u(t)),t∈[0,1],δ∈(3,4],{u(0)=u′(0)=u(1)=u′(1)=0在一致分数阶导数的定义下多个正解的存在性问题,并举出示例证明所得结论.

The boundary value problem of fractional differential equation is discussed by using fixed point index theory,as follow{u^(δ)(t)=f(t,u(t)),t∈[0,1],δ∈(3,4],{u(0)=u′(0)=u(1)=u′(1)=0.The existence of multiple positive solutions under the definition of conformable fractional derivative,and two concrete examples are given.