Non-local boundary value problem for an ordinary fractional differential equation with the Dzhrbashyan–Nersesyan operator

In this paper, we study a nonlocal boundary value problem with integral displacement for an ordinary differential equation of fractional order containing the Dzhrbashyan–Nersesyan operator. Equations containing such operators are more complex and interesting to study than classical differential equations, due to some features of the Dzhrbashyan–Nersesyan operator. Using methods of mathematical analysis and the theory of fractional equations, an explicit representation of the solution to this problem was constructed. The resulting solution is expressed through the Mittag-Leffler function, which is a generalization of the exponential function to the case of fractional powers.