[Seminar] "Mathematical analysis of generalized fractional viscoelastic models" by Prof. Hiromichi Itou

Geometric PDE and Applied Analysis Seminar (September 28, 2026)

Title: Mathematical analysis of generalized fractional viscoelastic models

Speaker: Prof. Hiromichi Itou (Chuo University)

Abstract: Viscoelastic materials arise in a wide range of fields, including engineering, biology, and geophysics. Examples include synthetic polymers, biological tissues, and concrete. In this talk, we discuss a mathematical model for nonlinear viscoelastic materials within the framework of infinitesimal strain theory in a quasi-static setting. Since the twentieth century, fractional calculus has been widely used to generalize classical viscoelastic models and to describe memory effects in materials. We introduce generalized fractional viscoelastic (GFV) models based on the Caputo fractional derivative. The constitutive relations are formulated through Volterra hereditary integrals, where the creep functions are represented by Mittag-Leffler functions rather than the classical Prony-series representation. For a boundary value problem associated with the GFV model, we establish the existence of a solution. This work is based on joint research with V. A. Kovtunenko (University of Graz) and M. Yamamoto (The University of Tokyo).