Bachelor Project Proposals

Several topics are possible, related to the courses Partial Differential Equations (C000802), Applied Functional Analysis (C001307) and Approximation Methods for Boundary Value Problems (C001497). These topics are under guidance of Prof. Dr. M. Slodička and Dr. K. Van Bockstal. Some examples of topics are given below. Other topics can be determined upon mutual agreement.

Fractional Calculus

A fractional derivative is a derivative of any arbitrary order (real or complex). The aim of this project is to give a historical overview on fractional calculus and to study the basic properties of the Riemann-Liouville fractional integral and derivative, and Caputo fractional integral and derivative.

Fractional Differential Equations

The goal of this project is to study fractional differential equations (generalization of ordinary differential equations to an arbitrary non-integer order) and methods to solve them (e.g. Laplace transform method).

Numerical approximations of fractional derivatives

For most fractional differential equations it is not possible to provide methods to compute the exact solutions analytically. Therefore, it is necessary to revert to numerical methods. The aim of this project is to study these numerical methods to approximate the Riemann-Liouville fractional derivative and the Caputo fractional derivative.