The existence of positive solutions of singular fractional boundary value problems
We discuss the existence of positive solutions for the singular fractional boundary value problem D?u+f(t,u,u?,D?u)=0 D ? u + f ( t , u , u ? , D ? u ) = 0 , u(0)=0 u ( 0 ) = 0 , u?(0)=u?(1)=0 u ? ( 0 ) = u ? ( 1 ) = 0 , where 2<?<3 2 < ? < 3 , 0<?<1 0 < ? < 1 . Here D? D ? is the standard RiemannLiouville fractional derivative of order ? ? , f f is a Carathodory function and f(t,x,y,z) f ( t , x , y , z ) is singular at the value 0 of its arguments x,y,z x , y , z .
riemannliouville fractional derivative fractional differential equation singular problem riemannliouville fractional integral fixed point theorem on cones