Use of fractional ntegrated-differentiation in the equations of electrodynamics of material environments

The paper briefly presents an analysis of the major historical milestones formation of the theory of dynamic processe. He showed that at the moment is clearly a failure of traditional models of physical, because a complete description of the processes of modern signal processing fields, and it is impossible with the aid of classical mathematics, obtained on the basis of representation of signals in spaces integral measures and smooth functions. To address these deficiencies and in connection with the creation of the general concept by B. Mandelbrot fractals many scientists had the idea of applying them in the field of radio and radar. And the use of the ideas of scale invariance - " scaling" and sections of modern functional analysis, are associated with set theory, the theory of fractional dimensionality, general topology, geometric measure theory and the theory of dynamical systems, further opened up great potential and new perspectives in the treatment of multidimensional signals and related scientific and technical areas, such as nonlinear hydroacoustics. For the application of formulas of classical mathematics of the obtained on the basis of representation of signals in spaces of integral -represented measures and smooth functions, the authors proposed the mathematical apparatus of the use of fractional integro- differential equations of electrodynamics in material media. It is based on the fractional calculus put integrodifferential operators Riemann-Liouville and Caputo. In solving the problem analysis of the properties of the electromagnetic field in the dielectric is necessary to consider the effect of fractal properties of the motion of charges in a dissipative medium to create an electromagnetic field, and my order fractional polynomial, which determines not only the fractal properties of the motion of the charges, but also, in some sense, fractal study characterizes the dissipative environment.