Article
Ufa Mathematical Journal
Volume 4, Number 4, pp. 54-67
Fractional differential equations: change of variables and nonlocal symmetries
Gazizov R.K., Kasatkin A.A., Lukashchuk S.Yu.
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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 considered, the corresponding prolongation formulae for infinitesimal operator of the group are constructed. Usage of prolongation formulae for finding nonlocal symmetries of equations and checking their admittance is demonstrated on a simple example of an ordinary fractional differential equation.