ABSTRACT
Conservation laws still are not widely used for investigation the properties of fractional differential equations. The main reason is the fact that most fractional partial differential equations such as fractional diffusion and transport equations, fractional kinetic equations, fractional relaxation equations do not have a Lagrangian. Thus, Noether's theorem and its fractional generalizations cannot be used for obtaining conservation laws for such equations. In this chapter, a new technique for constructing conservation laws is applied for fractional differential equations not having a Lagrangian in a classical sense. The technique uses the modern methods of Lie group analysis of fractional differential equations and employs the concept of nonlinear self-adjointness proposed for inter order differential equations.
