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 existe 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.