Journal
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
Volume 23, Issue 1-2, Pages 215-228Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/BF02831970
Keywords
Mittag-Leffler function; fractional Taylor's series; fractional derivative; optimal control; Hamilton-Jacobi equation; dynamical programming; fractional partial differential equation
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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.
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