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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...


Necessary condition for an Euler-Lagrange equation on time scales

Dryl, M.; Torres, D. F. M.

We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given. © 2014 Monika Dryl and Delfim F. M. Torres.


Control of a novel chaotic fractional order system using a state feedback techn...

Razminia, A.; Torres, D. F. M.

We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh-Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counter...


Hahn's symmetric quantum variational calculus

Brito da Cruz, A. M. C.; Martins, N.; Torres, D. F. M.

We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler{Lagrange type and a sufficient optimality condi- tion for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculu...


An expansion formula with higher-order derivatives for fractional operators of ...

Almeida, R.; Torres, D.F.M.

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, an...


Necessary optimality conditions for infinite horizon variational problems on ti...

Dryl, M.; Torres, D.F.M.

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and its nabla derivative, as well as a nabla indefinite integral that depends on the unknown function.


Existence of three positive solutions to some p-Laplacian boundary value problems

Sidi Ammi, M. R.; Torres, D. F. M.

We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales. © 2013 Moulay Rchid Sidi Ammi and Delfim F. M. Torres.


Gestational protein restriction induces CA3 dendritic atrophy in dorsal hippoca...

Lopes, A.; Torres, D. B.; Rodrigues, Ana João; Cerqueira, João; Pêgo, José M.; Sousa, Nuno; Gontijo, J. A. R.; Boer, P. A.

Studies have demonstrated that nutrient deficiency during pregnancy or in early postnatal life results in structural abnormalities in the offspring hippocampus and in cognitive impairment. In an attempt to analyze whether gestational protein restriction might induce learning and memory impairments associated with structural changes in the hippocampus, we carried out a detailed morphometric analysis of the hippo...


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 ...


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