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We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB)equation for fractional order dynamical systems in which a generalizedperformance index is considered for the related optimal control problem. Owingto the nonlocality of the fractional order operators, the classical HJBequation, in the usual form, does not hold true for fractional problems.Effectiveness of the proposed technique is illustrated through a numericalexample.

Fractional Order Version of the HJB Equation