Positive solutions for boundary value problems of singular fractional differential equations (Q2016618)

Summary: By using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem \[ {^CD^\alpha_{0+}} u+ f(t,u,{^CD^\nu_{0+}u} {^CD^\mu_{0+}u})+ g(t,u{^CD^\nu_{0+}u}, {^CD^\mu_{0+}u})= 0, \] \[ u(0)= u'(0)= u''(0)= u'''(0)= 0, \] where \(3<\alpha<4\), \(0<\nu< 1\), \(1<\mu<2\), \({^CD^\alpha_{0+}}\) is Caputo fractional derivative, \(f(t,x,y,z)\) is singular at the value \(0\) of arguments \(x\), \(y\), \(z\), and \(g(t,x,y,z)\) satisfies the Lipschitz condition.