## Rui Ferreira

## Lyapunov-type inequalities for fractional differential equations

We show how to obtain Lyapunov-type inequalities for boundary value problems depending on fractional differential operators, in which the order is a real

number between one and two. Moreover, we provide some insights on how to generalize these results for higher order differential equations.

number between one and two. Moreover, we provide some insights on how to generalize these results for higher order differential equations.

Raquel Pinto

## MDS 2D convolutional codes

Maximum Distance Separable (MDS) block codes and MDS one-dimensional (1D) convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this talk we generalize this concept

to the class of two-dimensional (2D) convolutional codes. For that we introduce a natural bound on the distance of a 2D convolutional code, which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then we prove the existence of 2D convolutional codes that reach such bound by presenting a concrete constructive procedure.

to the class of two-dimensional (2D) convolutional codes. For that we introduce a natural bound on the distance of a 2D convolutional code, which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then we prove the existence of 2D convolutional codes that reach such bound by presenting a concrete constructive procedure.

Delfim F. M. Torres

## Computational Methods in the Fractional Variational Calculus

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, allowing problem

modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems,

numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order

derivatives and generalized finite differences. Direct and indirect methods for solving fractional variational problems are presented.

modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems,

numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order

derivatives and generalized finite differences. Direct and indirect methods for solving fractional variational problems are presented.