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We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.

- Ivan Matychyn, Viktoriia Onyshchenko, Delfim F. M. Torres
- 2014

Linear fractional differential equations whose right hand side contains additive Dirac distributions are investigated. Analytical solutions to these equations are obtained on the basis of the Laplace transform method. AMS Subject Classifications: 34A08, 34A37.

- Ricardo Almeida, Delfim F. M. Torres
- Appl. Math. Lett.
- 2009

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

- Cristiana J. Silva, Delfim F. M. Torres
- Mathematical biosciences
- 2013

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure interventions. They depend on the parameters of the model and reduce effectively the number of active infectious and persistent… (More)

The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-α derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen’s inequality on time scales via… (More)

- Delfim F. M. Torres, MOULAY RCHID, Delfim F. M. Torres
- 2007

We make use of the Guo-Krasnoselskii fixed point theorem on cones to prove existence of positive solutions to a non local p-Laplacian boundary value problem on time scales arising in many applications. Acknowledgements: The authors were partially supported by the Portuguese Foundation for Science and Technology (FCT) through the Centre for Research in… (More)

We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found,… (More)

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann–Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of the theorems of Green and Gauss, fractional Euler–Lagrange equations, and fractional natural boundary… (More)

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal’s necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal’s Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for… (More)

- Delfim F. M. Torres
- Eur. J. Control
- 2002

We obtain a generalization of E. Noether’s theorem for the optimal control problems. The generalization involves a oneparameter family of smooth maps which may depend also on the control and a Lagrangian which is invariant up to an addition of an exact differential.