On the generalized boundary value problem for a linear ordinary delay differential equation with Dzhrbashyan–Nersesyan derivative

In this paper, a solution to a boundary value problem with generalized Sturm-type conditions for a linear ordinary delay differential equation with the Dzhrbashyan–Nersesyan fractional differentiation operator of arbitrary order, is constructed. For the problem under study, an explicit representation of the solution and a condition for unique solvability are obtained. An existence and uniqueness theorem is formulated. The solution to the problem is written out in terms of a special function $W_\nu (t)$, which is defined in terms of the generalized Mittag-Leffler function.