Generalized diffusion equation with nonlocality of space-time: Analytical and numerical analysis

We present a general approach for obtaining the generalized transport equations weakly nonequilibrium processes with fractional derivatives by using Liouville equation system of classical particles and Zubarev statistical operator method. A diffusion in is obtained processes. Based on non-Markov equation, taking into account spatial nonlocality modeling coefficient particle Dαα′(r,r′;t,t′)=W(t,t′)D̄αα′(r,r′) calculus, Cattaneo–Maxwell-type time space obtained. In case constant coefficient, analytical numerical studies frequency spectrum Cattaneo–Maxwell are performed. Numerical calculations phase group velocities change values characteristic relaxation time, indices temporal ξ α carried out.