Auxiliary Conditions To The Euler-Lagrange Equations For A New Class Of Non-Standard Lagrangians

A new class of non-standard Lagrangians that explicitly depend on the special functions of mathematical physics is discovered
and this requires adding some auxiliary conditions to the Euler-Lagrange equations. Several examples with applications of the
new non-standard Lagrangians are presented and discussed. Moreover, the relationships between the obtained results and Lie
algebras and Lie groups are also addressed.