Positive solutions of two-point boundary value problems for fractional singular differential equations (Q1760433)

The authors consider the fractional singular differential equation \[ D_{0^+}^{\alpha} u(t)+f(t,u(t))=0,\;0<t<1, \] satisfying the conjugate two point boundary conditions \[ u^{(i)}(0)=0,\;0\leq i\leq n-2,\;u(1)=0, \] where \(D_{0^+}^{\alpha}\) is the Riemann-Liouville fractional-order derivative. The authors obtain Green's function for the homogeneous boundary value problem corresponding to the above boundary value problem and establish inequalities involving the Green's function. They prove the existence of twin positive solutions for the two point boundary value problem.