A foundational approach to the Lie theory for fractional order partial differential equations

TL;DR

This paper extends classical Lie symmetry theory to fractional order partial differential equations, establishing a theoretical framework and prolongation formula for analyzing symmetries in these complex equations.

Contribution

It introduces a general prolongation formula and proves a Lie theorem for fractional PDEs, expanding symmetry analysis to fractional calculus.

Findings

Established a framework for Lie symmetry analysis of fractional PDEs

Proposed a prolongation formula for equations with multiple variables

Proved the Lie theorem in the context of fractional differential equations

Abstract

We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie symmetries in the case of an arbitrary finite number of independent variables. We also prove the Lie theorem in the case of fractional differential equations, showing that the proper space for the analysis of these symmetries is the infinite dimensional jet space.