Positive solutions for singular higher-order fractional differential equations with nonlocal conditions

Abstract

In this paper, by means of the fixed point index theorem in cones, under some weak conditions concerning the first eigenvalue corresponding to the relevant linear operator, the existence and multiplicity of positive solutions for a class of singular higher-order fractional differential equations with integral boundary conditions are investigated. The nonlinearity permits singularities not only at \(t=0,\,1\) but also at \(u=0\).