# Lie symmetry analysis of a class of time fractional nonlinear evolution systems

## TL;DR

This paper applies Lie symmetry analysis to a class of time fractional nonlinear evolution systems, providing a complete classification of symmetries and invariant solutions, and exploring the algebraic structures involved.

## Contribution

It offers a comprehensive symmetry classification and explicit invariant solutions for a class of time fractional PDEs, expanding understanding of their symmetry properties.

## Key findings

- The class of systems is divided into two cases based on the function type.
- The Lie algebra generated has dimension greater than 2 in each case.
- Explicit group invariant solutions are obtained for specific cases.

## Abstract

We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of group invariant solutions of this class of systems. We find that the class of systems of differential equations studied is naturally divided into two cases on the basis of the type of a function that they contain. In each case, the dimension of the Lie algebra generated by the infinitesimal symmetries is greater than 2, and for this reason we present the structures and one-dimensional optimal systems of these Lie algebras. The reduced systems corresponding to the optimal systems are also obtained. Explicit group invariant solutions are found for particular cases.