Towards the Formalization of Fractional Calculus in Higher-Order Logic

TL;DR

This paper discusses ongoing efforts to formalize fractional calculus within the HOL Light theorem prover, aiming to enhance mathematical rigor and facilitate applications in science and engineering.

Contribution

It introduces a formalization project for fractional calculus in higher-order logic, outlining motivation, methodology, current progress, and future plans.

Findings

Initial formalization framework established

Enhanced rigor in fractional calculus modeling

Roadmap for future formalization milestones

Abstract

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.