On one control problem of a variable structure with fractional Caputo derivatives

We consider an optimal control problem with a variable structure, described in different time intervals by various ordinary nonlinear fractional differential equations. Using an analogue of the incremental method, a necessary condition for first-order optimality is proved. In the case of convex control domains, a linearized maximum condition is proved, and in the case of open control domains, an analogue of the Euler equation is obtained.