Symmetries in Non-Smooth Settings

Symmetry group analysis is a powerful tool in the study of differential equations, in particular for determining invariance properties, constructing special solutions or deriving conservation laws in systems of physical interest. The theory of algebras of generalized functions (in the sense of Colombeau) efficiently deals with linear and nonlinear partial differential equations which involve singularities, with applications in such diverse fields as mathematical physics (general relativity, nonsmooth mechanics), nonlinear distributional geometry or global analysis. Fractional calculus extends many of the modelling capabilities of conventional calculus and integer-order differential equations. It deals with derivatives of any real (and even complex) order. This book attempts to provide a synthesis of these fields with the aim of reaching a global framework for symmetry group methods in non-smooth settings.