FRACTIONAL DIFFERENTIAL EQUATIONS: CHANGE OF VARIABLES AND NONLOCAL SYMMETRIES

Abstract

In this paper point transformations of variables in fractional integrals and derivatives of different types are considered. In the general case, fractional integro- differentiation of a function with respect to another function arises after such substitution. The problem of applying a point transformations group to this type of operators is con- sidered, the corresponding prolongation formulae for infinitesimal operator of the group are constructed. Usage of prolongation formulae for finding nonlocal symmetries of equa- tions and checking their admittance is demonstrated on a simple example of an ordinary fractional differential equation.