Аннотация
This paper considers a boundary value problem for a fractional-order differential equation in the sense of Caputo with an involutive transformation. The parametrization method of Professor D. Dzhumabaev is applied to solve the problem. A parameter is introduced, and a substitution is performed. Thus, the considered problem is divided into two parts: the Cauchy problem for a fractional-order differential equation and a linear equation with respect to the introduced parameter. The parameters are chosen in such a way that the Cauchy problem for the fractional-order differential equation has a classical solution. By applying certain transformations, a unique solution to the Cauchy problem is determined. Based on the unique solvability of the obtained equation concerning the introduced parameter, the solvability of the studied problem is established.