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Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function. (English) Zbl 1111.49014
Summary: By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange’s characteristics method (a new approach) for solving nonlinear fractional partial differential equations. The key of this results is the fractional Taylor’s series f(x+h)=E α (h α D α )f(x) where E α (·) is the Mittag-Leffler function.
49K15Optimal control problems with ODE (optimality conditions)
90C39Dynamic programming
60G18Self-similar processes
49L20Dynamic programming method (infinite-dimensional problems)
49K20Optimal control problems with PDE (optimality conditions)
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