Generalized Electrodiffusion Equation with Fractality of Space-Time: Experiment and Theory

Physical and technological principles of formation of clathrate structures for supramolecular electronics are given in this paper. It has been established that supramolecular nature of the "host-guest" conjunction, in general, and hierarchical architecture of the corresponding clathrates, in particular, provide realization of such an extraordinary effect as an optically or a magnetically controlled phenomenon of colossal "negative capacity" with a predicted frequency interval of manifestation, magnitude, and multiplicity. For the first time, the experimental confirmation of the behavior of the electretized fractal clathrate GaSe⟨β-CD⟨FeSO₄⟩⟩ as a dissipative element, which accumulates inductive energy, is demonstrated. A general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method within Renyi statistics is presented. New non-Markovian electrodiffusion equations for ions in a spatially heterogeneous medium with the fractal structure and a generalized Cattaneo-type diffusion equation taking into account the fractality of space-time are obtained. The model of subdiffusion impedance based on the Cattaneo equation with fractional derivatives is applied to multilayer nanostructures. Nyquist diagrams for different valuses of the parameter τ (delay time of a flow relative to a concentration gradient) and the subdiffusion coefficient D_α are calculated.