We give a procedure to find a solution to the equation $D^{\alpha } _{b^{-}} D^{\alpha }_{0^{+}} y(x) + mD^{\alpha } _{0^{+}} D^{\alpha }_{b^{-}} y = C_{0}(x), \; 0 < x < b, \; 0 < \alpha < 1,$ solving the corresponding Fredholm integral equation of the second kind.