On a system of equations arising in viscoelasticity theory of fractional type

TL;DR

This paper investigates a system of PDEs with fractional derivatives in viscoelasticity, introducing a novel approach using quotient relations in the constitutive equation, and proves existence and uniqueness of solutions.

Contribution

It presents a new method for analyzing viscoelastic systems by considering quotient relations, extending the mathematical framework for fractional PDEs in this context.

Findings

Established existence and uniqueness of solutions for the PDE system.

Proposed a new approach using quotient relations in constitutive equations.

Applied the method to a viscoelastic rod with finite mass.

Abstract

We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in the constitutive equation instead the constitutive equation itself. Both, a rod and a body are assumed to have finite mass. The motion of a body is assumed to be translatory. Existence and uniqueness for the corresponding initial-boundary value problem is proved within the spaces of functions and distributions.