Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations

Abstract EN

In this paper, by using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem DC0+αu+ft,u,DC0+νu,DC0+μu+gt,u,DC0+νu,DC0+μu=0, u0=u′0=u′′0=u′′′0=0, where 3<α<4, 0<ν<1, 1<μ<2, DC0+α is Caputo fractional derivative, ft,x,y,z is singular at the value 0 of its arguments x,y,z, and gt,x,y,z satisfies the Lipschitz condition.