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We consider an optimal control problem for a dynamical system described by aCaputo fractional differential equation and a terminal cost functional. Weprove that, under certain assumptions, the (non-smooth, in general) valuefunctional of this problem has a property of directional differentiability oforder $\alpha$. As an application of this result, we propose a new method forconstructing an optimal positional (feedback) control strategy.

Sensitivity analysis of value functional of fractional optimal control problem with application to construction of optimal feedback control