Predavanje Sanje Konjik
lokacija:
PMF Split
vrijeme:
21.04.2023 - 12:00 - 13:00
U organizaciji znanstvenog razreda Splitskog matematičkog društva
dr. sc. Sanja Konjik
Odjel za matematiku i fiziku
Prirodno-matematički fakultet
Sveučilište u Novom Sadu
će održati predavanje pod naslovom:
FRACTIONAL CALCULUS AND THE WAVE EQUATION
Predavanje će se održati u petak 21.4. od 12h u dvorani B3-17 Odjela za matematiku PMF-a, Ruđera Boškovića 33.
Pozivamo sve zainteresirane da prisustvuju predavanju.
Sažetak:
Fractional calculus is a powerful tool for modeling phenomena arising in diverse fields such as physics, mechanics, engineering, economics, medicine, biology, chemistry, etc. It deals with derivatives and integrals of arbitrary real (or even complex) order, thus extending capabilities of the classical calculus, but also introducing novelties in theoretical and applied research. For instance, fractional derivatives more accurately describe properties of viscoelastic materials than the integer order ones. This is of particular interest in the study of wave propagation in viscoelastic media.
In this talk we present a generalization of the wave equation within the framework of fractional calculus. The approach is based on fractionalization (i.e., substitution of the integer order derivatives with the fractional ones) of the stress-strain constitutive equation in the model of wave propagation in elastic media, with the aim of preserving the physical meaning of the model. We propose the fractional Zener constitutive relation, and then study the existence and uniqueness of a fundamental solution for the corresponding generalized Cauchy problem. Also, we provide numerical examples in order to illustrate theoretical results.
