Symmetry properties for systems of two ordinary fractional differential equations

Abstract

Lie point symmetries of two systems of ordinary fractional differential equations with the Riemann–Liouville derivatives are considered. Infinite algebra $L$ of equivalence transformation operators is constructed. It is shown that all admitted operators generate some subalgebra in $L$ and classification of systems with respect to point symmetries can be based on the optimal system of subalgebras. The optimal system of one-dimensional $L$ subalgebras and the complete normalized optimal system for its finite-dimensional part $L_6$ are constructed.