investigation of a common solution for a multi-singular fractional system by using control functions method

In this article, first of all, we investigate a pointwise defined multi-singular fractional differential equation. using control functions method, existence a solution for the problem, will be proved. in the following, we determine some conditions to prove the existence of a common solution for two multi-singular fractional differential equations with integral boundary conditions. to this purpose, we use inequalities, control functions and fixed point method. finally, an example will illustrate our main results.