A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives
arXiv:1402.3730
Abstract
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we rewrite the fractional problem into a classical optimal control problem. The latter problem is then solved by application of standard numerical techniques. We illustrate the procedure with an example.
This is a preprint of a paper whose final and definite form will appear in International Journal of Difference Equations, ISSN 0973-6069 (See http://campus.mst.edu/ijde). Submitted Nov 23, 2013; Revised Jan 27, 2014; Accepted Feb 15, 2014
References in corpus (5)
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- Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
- Discrete Direct Methods in the Fractional Calculus of Variations
- Leitmann's direct method for fractional optimization problems
- Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control