Existence of positive solutions for the boundary value problem of nonlinear fractional differential equations

In this paper, we investigate the nonlinear differential equation of fractional order.CD0+αu(t)=f(t,u(t),u′(t)),1<α⩽2,0

► We study fractional differential equations with the Caputo derivative.
► The first order u′(t) is involved in the nonlinear term explicitly.
► In this paper, unlike [3], the singularity is not inherent any more.
► By means of Schauder’s fixed point theorem, a new theorem is established.
► By means of Krasnoselskii’s fixed point theorem, another theorem is obtained.