Positive solutions to integral boundary value problems for singular delay fractional differential equations

Delay fractional differential equations play very important roles in mathematical modeling of real-life problems in a wide variety of scientific and engineering applications. The objective of this manuscript is to study the existence and uniqueness of positive solutions for singular delay fractional differential equations with integral boundary data. To investigate the described system, we construct a $u_0$-positive operator first. New research technique of by constructing $u_0$-positive operator is used to overcome the difficulties caused by both the delays and the boundary value conditions. Then the sufficient conditions for the existence and uniqueness of positive solutions of a class of the singular delay fractional differential equations with integral boundary is proved by using the fixed point theorem in cone.