Existence and uniqueness of positive solution to singular fractional differential equations

摘要

In this paper, we discuss the existence and uniqueness of a positive solution to the following singular fractional differential equation with nonlocal boundary value conditions:{D0+αu(t)+f(t,u(t))=0,0t1,u(0)=0,D0+βu(1)=∑i=1m−2ηiD0+βu(ξi),where1α≤2,0βα−1,0ξ1⋯ξm−21with∑i=1m−2ηiξiα−β−11,D0+αis the standard Riemann-Liouville derivative, f may be singular att=0,t=1, andu=0. MSC:34B10, 34B15.