Abstract:
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.
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