Fractional wave equations: hereditariness and non-locality
Dušan Zorica (Serbian Academy of Arts and Sciences)
Thursday 22nd October, 2020 14:00-15:00 ZOOM (ID: 978 1364 3992)
Topic: Applied Mathematics Seminar Dusan Zorica
Start Time : Oct 22, 2020 01:48 PM
Passcode: See the e-mail with subject: Seminar recording password
The generalization of classical wave equation is performed within the framework of fractional calculus in order to account for the hereditariness and non-locality representing the material features. Both effects are included through the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through distributed-order fractional constitutive equation generalizing all linear models having differentiation orders up to order one, while in the case of differentiation orders exceeding the first order, the fractional Burgers model is considered. Moreover, a priori energy estimates are used in order to prove dissipativity property of the hereditary fractional wave equations and energy conservation property for two non-local fractional wave equations. Moreover, microlocal approach in analyzing the singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.