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The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application. (English) Zbl 1192.34008
The authors discuss some new positive properties of the Green function for boundary value problems of nonlinear Dirichlet-type fractional differential equation
\[ \begin{aligned} &D_{0^+}^{\alpha}u(t)+f(t,u(t))=0,\quad 0<t<1,\\ &u(0)=u(1)=0 \end{aligned} \] Applications are also given.
Reviewer: Minghe Pei (Jilin)

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34B27 Green’s functions for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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