Journal of applied mathematics & informatics
- Volume 23 Issue 1_2
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- Pages.215-228
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- 2007
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
FRACTIONAL HAMILTON-JACOBI EQUATION FOR THE OPTIMAL CONTROL OF NONRANDOM FRACTIONAL DYNAMICS WITH FRACTIONAL COST FUNCTION
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 non linear fractional partial differential equations. The key of this results is the fractional Taylor's series
Keywords
- Mittag-Leffler function;
- fractional Taylor's series;
- fractional derivative;
- optimal control;
- Hamilton-Jacobi equation;
- dynamical programming;
- fractional partial differential equation