On the question of solving a mixed boundary value problemfor an equation with fractional derivatives with different origins

An approach to solving boundary value problems for an ordinary differential equation of fractional order containing a composition of left- and right-handed Riemann-Liouville and Caputo fractional differentiation operators is proposed. The approach is based on the reduction of the equation under consideration to the study of integral equations of fractional order with involution. As an example, a mixed problem has been solved. In particular, the proposed approach allows us to improve the previously obtained conditions for the solvability of this problem.