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[CT015]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In joint work with Dr. Kateryna Marynets, we adapt a numerical-analytic technique for constructing approximations to a system of nonlinear fractional differential equations with integral boundary conditions. The boundary conditions are parametrized, and the parameter values, which govern the solution’s behavior, are calculated numerically. The convergence of the method is improved using a dichotomy-type approach, and its applicability is extended to a wider class of problems. Our results are confirmed by a model example.
Classification : 34A08, 34B10, 37M99, Fractional boundary value problems
Author(s) :
- Dona Pantova (TU Delft)
- Kateryna Marynets (TU Delft)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, an optimal control problem is considered in which a motion of a dynamical system is described by differential equations with Caputo fractional derivatives and the goal of control is to minimize a Bolza cost functional. The problem is associated with a Hamilton - Jacobi - Bellman equation with so-called fractional coinvariant derivatives. Results concerning viscosity solutions of this equation and their application to the construction of an optimal feedback control are discussed.
Classification : 34A08, 49L12, 93B52, 49L25
Author(s) :
- Mikhail Gomoyunov (N.N. Krasovskii Institute of Mathematics and Mechanics)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, a fast finite difference scheme is discussed to a hidden-memory variable-order time-fractional diffusion equation. To reduce the computational cost and memory, a modified exponential-sum-approximation method is utilized to discretize the hidden-memory variable-order fractional derivative. We then develop different techniques from the analysis of L1 methods to prove the convergence for the corresponding fast fully discrete scheme. Numerical experiments are presented to substantiate the theoretical results.
Classification : 34A08, 26A33, 65D15, 65D40
Author(s) :
- Lu-Yao Sun (University of Macau)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Compartment models are a widely used class of models that are useful when considering the flow of objects or people or energy between different labelled states, referred to as compartments. Recently we have constructed a general framework for fractional order compartment models, where the governing equations involve fractional order derivatives, via the consideration of a semi-Markov stochastic process. Here we show extensions to this approach to obtain more general operators.
Classification : 34A08, 60K40, 92C45
Author(s) :
- Christopher Angstmann (University of New South Wales)
- Bruce Henry (University of New South Wales)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Despite the recent medical advances, treatments are unsuccessful in 15-20% of cases in Acute Lymphoblastic Leukemia ( ALL ) patients. The main aim of our study is to analyse data from bone marrow samples and to use artificial intelligence to improve current techniques of diagnosis in ALL protocols. Using machine learning techniques, our results predict bone marrow behavior and allow us to classify patients depending on their relapse risk.
Classification : 34A12, 92-10
Author(s) :
- Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
- Salvador Chulián (University of Cádiz)
- Álvaro Martínez-Rubio (Department of Mathematics, Universidad de Cádiz)
- María Rosa (Department of Mathematics, Universidad de Cádiz)