Variational formulation for fractional hyperbolic problems in the theory of viscoelasticity

TL;DR

This paper develops a variational framework for fractional hyperbolic equations in viscoelasticity, establishing existence, uniqueness, and estimates for weak solutions using the Galerkin method.

Contribution

It introduces a new variational formulation for fractional hyperbolic problems in viscoelasticity, linking mathematical theory with physical quantities.

Findings

Established existence and uniqueness of weak solutions.

Provided a priori estimates for solutions.

Developed a functional setting aligned with physical quantities.

Abstract

In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary viscoelasticity is studied. An appropriate functional setting is introduced in order to establish the existence, uniqueness and a priori estimates for weak solutions. This framework is developed in close concordance with important physical quantities of the theory of viscoelasticity