In this paper we consider Nash equilibria for the affine linear quadratic fractional differential game for a finite planning horizon where the dynamic system depends on Caputo fractional derivatives. The Nash equilibrium is a proposed solution of a noncooperative game involving two or more players in which each player assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. According to the Pontryagin minimum principle for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In order to solve this problem, we can use any optimization algorithms.

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