[00336] Recent advances in Optimization methods with applications
Session Time & Room : 1E (Aug.21, 17:40-19:20) @F312
Type : Proposal of Minisymposium
Abstract : The aim of this session is to present recent advances in optimization (e.g. calculus of variations, control theory, decision theory, etc). We are interested in its different approaches: theoretical, numerical analysis or applications to real life. Potential topics include, but are not limited to: Optimization, Numerical Mathematics, Optimal Control, Calculus of Variations, consensus theory, Mathematical Modeling, Dynamical Systems, Applications to Physics, Biology, Medicine and Robotics, and fractional calculus.
[02720] HABITAT LOSS AND COOPERATIVE HUNTING ON A THREE-SPECIES TROPHIC SYSTEM
Format : Talk at Waseda University
Author(s) :
Jorge Duarte (Instituto Superior de Engenharia de Lisboa)
Cristina Januário (Instituto Superior de Engenharia de Lisboa)
Nuno Martins (Instituto Superior Tecnico)
Abstract : Changes in ecosystems progress at a rapid pace mainly due to the climate crisis and human-induced perturbations. Researchers have used mathematical models to understand how species respond to these changes in habitat in order to ultimately forecast species extinctions and develop efficient conservation strategies. Our work highlights the fragility of predators hunting cooperatively under the loss of habitat.
[02816] Modeling of impulsive perturbations by generalized fractional differential equations
Format : Talk at Waseda University
Author(s) :
Snehana Hristova (Plovdiv University)
Abstract : The main aim is to emphasize on the statement of the impulsive perturbations in fractional differential equations. It will be considered two types of impulses- instantaneous impulses and non-instantaneous ones. To be more general we will consider the generalized proportional fractional derivatives of both Caputo type and Riemann-Liouville type in differential equations. Some existence results as well as stability properties of the solutions will be presented.
[02710] Necessary conditions to optimize functionals involving a generalized fractional derivative
Format : Talk at Waseda University
Author(s) :
Ricardo Almeida (University of Aveiro)
Abstract : In this work we combine two ideas: fractional derivatives of variable order and fractional derivatives depending on another function. With such operators, we develop a variational problem theory by presenting necessary conditions of optimization. The fundamental problem will be addressed, proving an Euler-Lagrange equation, and then other versions will be considered such as the isoperimetric problem or the Herglotz problem. An integration by parts formula is also proven. To end, we provide a numerical tool to solve fractional problems dealing with such fractional derivatives. The main idea is to approach the fractional derivative by an expansion formula in terms of integer order derivatives and then rewrite the fractional problema as a classical one.
[02725] Herglotz’s Variational Problem involving distributed-order fractional derivatives with arbitrary kernels
Format : Talk at Waseda University
Author(s) :
Natália Martins (University of Aveiro)
Abstract : In this talk we extend the study of fractional variational problems of Herglotz type for the case where the Lagrangian
function depends on distributed-order fractional derivatives with arbitrary smooth kernels, the endpoints conditions,
and a real parameter. The fact that the Lagrangian depends on the boundary conditions and
an arbitrary parameter is not an artificial generalization, as this formulation is important in many problems, such as in physics and economics.
