Existence of a unique positive solution for a singular fractional boundary value problem

Karimov, E. T. and Sadarangani, K.



In the present work, we discuss the existence of a unique positive solution of a boundary value problem for a nonlinear fractional order equation with singularity. Precisely, order of equation D_{0+}^\alpha u(t)=f(t,u(t)) belongs to (3,4] and f has a singularity at t=0 and as a boundary conditions we use u(0)=u(1)=u'(0)=u'(1)=0. Using a fixed point theorem, we prove the existence of unique positive solution of the considered problem.

Additional Information


Karimov, E. T., Sadarangani, K.