On the necessary optimality conditions for the fractional Cucker–Smale optimal control problem

•Study of sparse flocking control for the fractional Cucker–Smale multi-agent model.•Taking into consideration history or memory dependency in the selforganization of the group by applying the approach (for designing the Cucker–Smale model) with fractional derivative.•Proof of the Pontryagin Maximum Principle (PMP) for the Lagrange optimal control problem governed by a multi-order control system with the Caputo derivative.•Applying the PMP to the fractional Cucker–Smale optimal control problem. We provide necessary optimality conditions for external control with limited strength. This external controller by acting only on a few agents enforces flocking in the multi- agent system.•Analysis of some particular problems illustrated by numerical examples. This paper develops a sparse flocking control for the fractional Cucker–Smale multi-agent model. The Caputo fractional derivative, in the equations describing the dynamics of a consensus parameter, makes it possible to take into account in the self-organization of group its history and memory dependency. External control is designed based on necessary conditions for a local solution to the appropriate optimal control problem. Numerical simulations demonstrate the effectiveness of the control scheme.