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1

Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

Chidouh A., Torres D. F. M.

Opuscula Mathematica

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2018

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Vol. 38, no. 1

31--40

EN

We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.

2

Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations

Yang X.-J., Srivastava H. M., Torres D. F. M., Zhang Y.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

409--417

EN

We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is considered and non-differentiable solutions for special cases obtained.

3

Optimal control for a steady state dead oil isotherm problem

Sidi Ammi M. R., Malinowska A. B., Torres D. F. M.

Control and Cybernetics

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2013

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Vol. 42, no. 2

459--470

EN

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optima control are proved, as well as necessary optimality conditions.

4

A time-scale variational approach to inflation, unemployment and social loss

Dryl M., Malinowska A. B., Torres D. F. M.

Control and Cybernetics

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2013

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Vol. 42, no. 2

399-418

EN

Both inflation and unemployment inflict social losses. When a tradeoff exists between the two, what would be the Best combination of inflation and unemployment? A well known approach in economics to address this question is writing the social loss as a function of the rate of inflation p and the rate of unemployment u, with different weights, and then, using known relations between p, u, and the expected rate of inflation π, to rewrite the social loss function as a function of π. The answer is achieved by applying the calculus of variations in order to find an optimal path π that minimizes Total social loss over a given time interval. Economists dealing with this question use a continuous or a discrete variational problem. Here we propose to use a time-scale model, unifying the results available in the literature. Moreover, the new formalism allows for obtaining new insights into the classical models when applied to real data of inflation and unemployment.

5

A generalized fractional calculus of variations

Odzijewicz T., Malinowska A. B., Torres D. F. M.

Control and Cybernetics

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2013

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Vol. 42, no. 2

443--458

EN

We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, transversality conditions for free boundary value problems, and a generalized Noether type theorem.

6

The delta-nabla calculus of variations

Malinowska A. B., Torres D. F. M.

Fasciculi Mathematici

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2010

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Nr 44

75-83

EN

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.