PHOTOS: doctoral defence – Hanna Britt Soots "Collocation based approximations for fractional differential equations"

On August 26th Hanna Britt Soots defended her thesis "Collocation based approximations for fractional differential equations".

Supervisors:

Professor Arvet Pedas, University of Tartu

Lecturer Kaido Lätt, University of Tartu

Opponents:

Luigi Brugnano, University of Firenze (Italy)

Martin Stynes, Beijing Computational Science Research Center (China)

Summary

Usually, when we talk about the derivative of a function y = f(t) we usually refer to an integer-order derivative: y’, y’’, y’’’, and so on. However, the question arises - can the order of a derivative be a positive real number or even a complex number? It turns out that this is indeed possible, and such a derivative, whose order is not generally an integer, is called a fractional-order derivative. Fractional differential equations have demonstrated strong potential in accurately modeling memory-dependent and hereditary behaviours in complex materials and dynamic systems. For example, fractional derivatives have found applications in biomedicine, economics, mechanics, and in the study of chaotic systems. Due to the complexity of finding exact solutions to equations involving fractional-order derivatives, the analysis and development of numerical methods is an important area of research. However, solving differential equations with fractional-order derivatives presents significant analytical and computational challenges, particularly due to the potentially singular behavior of their solutions. This dissertation investigates various fractional differential and integro-differential equations and studies the existence, uniqueness, and regularity of their solutions. Obtained results are illustrated with numerical examples.