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Fractional order optimal control problems with free terminal time
Pooseh, S.; Almeida, R.; Torres, D. F. M.We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal- time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimal...
Fractional variational problems depending on indefinite integrals
Almeida, R.; Pooseh, S.; Torres, D.F.M.We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and natural boundary conditions, which provide a generalization of the previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and dependi...
Approximation of fractional integrals by means of derivatives
Pooseh, S.; Almeida, R.; Torres, D. F. M.We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class C-n, n is an element of N, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional ...
Expansion formulas in terms of integer-order derivatives for the Hadamard fract...
Pooseh, S.; Almeida, R.; Torres, D. F. M.We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of the approximation method.
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