INVARIANCE OP INTEGRO-DIFFERENTIAL EQUATIONS WITH MOVING REGION OF INTEGRATION

摘要

General criterion of invariance of integro-differential equations under the Lie symmetry group of point transformations is derived. It is a generalization of the previous form of the criterion to the case of a moving range of integration. This is the situation when a region of integration depends on external, with respect to integration, variables what leads to its explicit dependence on a group parameter, so the region of integration moves under symmetry transformations. General case of dependence on independent and dependent variables and their derivatives is considered.