We use numerical simulations to study reaction-diffusion problems with diffusion driven by fractional Laplacian. Fractional Laplacian appears, e.g., in mathematical models of population dynamics where the dispersion of individuals is due to the so called Levy flights rather than due to Brown...

In this thesis we investigate applications of the Lovász local lemma and its related methods. We are going to describe the gradual development of these methods and show the specific examples of its use in the field of research on independent transversals and hypergraphs.

This Bachelor thesis deals with the Fučík spectrum of $p$-Laplace operator. We examine a nonlocal boundary value problem, with one Dirichlet boundary condition and one integral boundary condition. We implicitly describe the Fučík spectrum, we also appoximate it numerically and based on ...

This thesis is focused on option pricing in stochastic volatility models using neural networks. First, option prices in the Heston model are generated using the Heston-Lewis formula. A neural network is then trained using these prices to first estimate the parameters of the Heston&...

This paper deals with a BVP for a system which consists of two ordinary differential equations of the second order with concave and convex nonlinearities and Dirichlet boundary conditions. One of the equations contains a positive parameter $\lambda$. The aim of this work is&#x...