On fractional calculus and its variable-order generalization

In this presentation I will provide a brief overview on the origin of Fractional Calculus and its current rigorous formulation. I will then discuss some physical motivations for the generalisation of this theory to the variable-order case. Then I will introduce a novel perspective on variable-order fractional calculus, its precise formulation in terms of the General Fractional Calculus framework, and I will discuss some of its implications considering the fractional relaxation equation as a case study. Lastly, I will discuss an application of the proposed formalism to the theory of viscoelasticity.