Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function |
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Authors: | Guy Jumarie |
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Institution: | 1. Department of Mathematics, University of Quebec at Montreal, DowntownStation, P.O. Box 8888, H3C 3P8, Montreal, Qc, Canada
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Abstract: | 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 seriesf(x + h) = E α(hαDα)f(x) whereE α(·) is the Mittag-Leffler function. |
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