FRACTIONAL HAMILTON-JACOBI EQUATION FOR THE OPTIMAL CONTROL OF NONRANDOM FRACTIONAL DYNAMICS WITH FRACTIONAL COST FUNCTION

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-alpha(h(alpha)D(alpha)) f(x) where E-alpha(.) is the Mittag-Leffler function.