Scientific seminar on the differential and functional differential equation on topic "Boundary Value Problems for the Fractional Order Advection-Diffusion Equation" (chair: Professor A.L. Skubachevskii)

 

We will discuss the existence theorem for solutions to inhomogeneous one-dimensional and multidimensional fractional differential equations of advective diffusion with constant and variable coefficients, which arise in the description of many physical processes of stochastic transfer when studying fluid filtration in a highly porous (fractal) medium. The solution of the problem is obtained by the method of separation of variables (Fourier method). Fractional derivative operators in the sense of Caputo and Riemann-Liouville are considered. It is proved that the found solution of the boundary value problem satisfies the given boundary conditions. Eigenvalues and eigenfunctions of a boundary value problem for a second-order differential equation containing a fractional differentiation operator in the Riemann—Liouville sense are obtained and analyzed by analytical methods. The latter task is used to analyze the damping properties of various viscoelastic materials.