A Pontryagin maximum principle analogue in the optimal control problem of a differential equations system with a fractional Caputo derivative and a multipoint quality criterion

The processes optimal control problem described by a ordinary differential equations system with fractional order is considered. The quality criterion is a multipoint nonlinear functional. A quality functional increment formula is constructed by introducing a conjugate system in the fractional integral equation form such as Volterra. The necessary optimality condition is proved in the Pontryagin maximum principle analogue form by the constructed formula investigating with using the McShane needle variation.